If $A$ is a square matrix of order $3$ and $|A| = 5$, then the value of $|2A\ '|$ is:
- A$-10$
- B$10$
- C$-40$
- ✓$40$
Answer: D.
View full solution →Question types
Matrices question types
414 questions across 9 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
414
Questions
9
Question groups
5
Question types
01
M.C.Q (1 Marks)
239 Q→02Assertion (A) & Reason (B) MCQ
26 Q→031 Marks Question
31 Q→042 Marks Questions
52 Q→053 Marks Question
20 Q→065 Marks Questions
4 Q→07Case study (4 Marks)
8 Q→08Fill In The Blanks[1 Marks ]
14 Q→09True False[1 Marks ]
20 Q→Sample Questions
Matrices questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $A$ is a square matrix such that $A ^2= A,$ then $(I-A)^3+ A$ is equal to:
- ✓$I$
- B$0$
- C$I - A$
- D$I + A$
Answer: A.
View full solution →If $\text{A}=\begin{bmatrix}\text{n}&0&0\\0&\text{n}&0\\0&0&\text{n}\end{bmatrix}$ and $\text{B}=\begin{bmatrix}\text{a}_1&\text{a}_2&\text{a}_3\\\text{b}_1&\text{b}_2&\text{b}_3\\\text{c}_1&\text{c}_2&\text{c}_3\end{bmatrix},$ then $AB$ is equal to:
- A$B$
- ✓$n^B$
- C$B^n$
- D$A + B$
Answer: B.
View full solution →If $A$ is a square matrix, then $AA$ is $a:$
- ASkew$-$symmetric matrix.
- BSymmetric matrix.
- CDiagonal matrix.
- ✓None of these.
Answer: D.
View full solution →The restriction on $n, k$ and $p$ so that $PY + WY$ will be defined are:
- ✓$k = 3, p = n$
- B$k$ is arbitary$, p = 2$
- C$p$ is arbitary$, k = 3$
- D$k = 2, p = 3$
Answer: A.
View full solution →Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: Let $\text{A}_{\theta}=\begin{pmatrix}\cos\theta+\sin\theta&\sqrt{2}\sin\theta\\-\sqrt{2}\sin\theta&\cos\theta-\sin\theta\end{pmatrix}\Big(\text{A}_{\frac{\pi}{3}}\Big)^{3}=-\text{I}.$
Reason: $\text{A}_{\theta}\cdot\text{A}_{\phi}=\text{A}_{\theta+\phi}.$
Assertion: Let $\text{A}_{\theta}=\begin{pmatrix}\cos\theta+\sin\theta&\sqrt{2}\sin\theta\\-\sqrt{2}\sin\theta&\cos\theta-\sin\theta\end{pmatrix}\Big(\text{A}_{\frac{\pi}{3}}\Big)^{3}=-\text{I}.$
Reason: $\text{A}_{\theta}\cdot\text{A}_{\phi}=\text{A}_{\theta+\phi}.$
- ✓Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- BBoth $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Answer: A.
View full solution →Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as:
Assertion: If $\text{A}=\begin{pmatrix}0 & 2 & -1\\ -2 & 0 & 3 \\ 1& -3 & 0 \end{pmatrix},$ then $A^{-1}$ is symmetric matrix.
Reason: If $A$ is skew symmetric matrix then $A^{-1}$ is skew symmetric matrix.
Assertion: If $\text{A}=\begin{pmatrix}0 & 2 & -1\\ -2 & 0 & 3 \\ 1& -3 & 0 \end{pmatrix},$ then $A^{-1}$ is symmetric matrix.
Reason: If $A$ is skew symmetric matrix then $A^{-1}$ is skew symmetric matrix.
- ✓Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- BBoth $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Answer: A.
View full solution →Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: If $A$ is a square matrix such that $A^2 = I, $ then $(I + A)^2 - 3A = I.$
Reason: $Al = IA = A,$ where $I$ is Idetity matrix.
Assertion: If $A$ is a square matrix such that $A^2 = I, $ then $(I + A)^2 - 3A = I.$
Reason: $Al = IA = A,$ where $I$ is Idetity matrix.
- ABoth $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- BBoth $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C$A$ is true but $R$ is false.
- ✓$A$ is false but $R$ is true.
Answer: D.
View full solution →Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: If $\text{A}=\begin{pmatrix}3&-2&10\\-2&4&5\\10&5&6\end{pmatrix}$ and $\text{x}=\begin{pmatrix}1&5&6\\-2&0&1\\4&3&2\end{pmatrix} X\ 'AX$ is symmetric matrix.
Reason: $X\ 'AX$ is symmetric or skew symmetric as $A$ is symmetric or skew symmetric.
Assertion: If $\text{A}=\begin{pmatrix}3&-2&10\\-2&4&5\\10&5&6\end{pmatrix}$ and $\text{x}=\begin{pmatrix}1&5&6\\-2&0&1\\4&3&2\end{pmatrix} X\ 'AX$ is symmetric matrix.
Reason: $X\ 'AX$ is symmetric or skew symmetric as $A$ is symmetric or skew symmetric.
- ✓Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- BBoth $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Answer: A.
View full solution →Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as:
Assertion: If $\text{A}=\begin{pmatrix}1 & 2 & -1\\ 2 & 0 & 3 \\ -1& 3 & 4 \end{pmatrix},$ then $A^{-1}$ is symmetric matrix.
Reason: If $A$ is symmetric matrix then $A^{-1}$ is symmetric matrix.
Assertion: If $\text{A}=\begin{pmatrix}1 & 2 & -1\\ 2 & 0 & 3 \\ -1& 3 & 4 \end{pmatrix},$ then $A^{-1}$ is symmetric matrix.
Reason: If $A$ is symmetric matrix then $A^{-1}$ is symmetric matrix.
- ✓Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
- BBoth $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Answer: A.
View full solution →If $A=\left[\begin{array}{cc} {\alpha} & {\beta} \\ {\gamma} & {-\alpha} \end{array}\right]$ is such that $A^2 = I,$ then
View full solution →If A is square matrix such that $A^2 = A,$ then $(I + A)^3 – 7\ A$ is equal to
View full solution →If the matrix A is both symmetric and skew symmetric, then
For the matrix $A=\left[\begin{array}{ll} {1} & {5} \\ {6} & {7} \end{array}\right]$, verify that (A – A′) is a skew-symmetric matrix
View full solution →Show that the matrix $A=\left[\begin{array}{rrr} {0} & {1} & {-1} \\ {-1} & {0} & {1} \\ {1} & {-1} & {0} \end{array}\right]$is a skew-symmetric matrix.
View full solution →For what values of $x : \left[\begin{array}{lll}{1} & {2} & {1}\end{array}\right] \left[\begin{array}{lll}{1} & {2} & {0} \\ {2} & {0} & {1} \\ {1} & {0} & {2}\end{array}\right]\left[\begin{array}{l}{0} \\ {2} \\ {x}\end{array}\right] = 0.$
View full solution →Show that the matrix B’AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.
If A and B are symmetric matrices, prove that AB – BA is a skew symmetric matrix.
For the matrix $A=\left[\begin{array}{ll} {1} & {5} \\ {6} & {7} \end{array}\right]$, verify that (A + A′) is a symmetric matrix.
View full solution →If $A=\left[\begin{array}{cc} {\sin \alpha} & {\cos \alpha} \\ {-\cos \alpha} & {\sin \alpha} \end{array}\right]$, then verify that A′ A = I
View full solution →Find the matrix $X$ so that $X\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6\end{array}\right]=\left[\begin{array}{ccc}-7 & -8 & -9 \\ 2 & 4 & 6\end{array}\right]$
View full solution →A manufacturer produces three products, x, y, z which he sells in two markets. Annual sales are indicated below:
| Market | Products | ||
| I | 10000 | 2,000 | 18,000 |
| II | 6000 | 20,000 | 8,000 |
- If unit sale prices of x, y and z are Rs 2.50, Rs 1.50 and Rs 1.00 respectively, find the total revenue in each market with the help of matrix algebra.
- If the unit costs of the above three commodities are Rs 2.00, Rs 1.00 and 50 paise respectively. Find the gross profit.
Find $x$, if $\left[\begin{array}{lll}x & -5 & -1\end{array}\right]\left[\begin{array}{lll}1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3\end{array}\right]\left[\begin{array}{l}x \\ 4 \\ 1\end{array}\right]=0$
View full solution →If $A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]$ show that $\mathrm{A}^2-5 \mathrm{~A}+7 \mathrm{I}=0$
View full solution →Find the values of $\mathrm{x}, \mathrm{y}, \mathrm{z}$ if the matrix $A=\left[\begin{array}{ccc}0 & 2 y & z \\ x & y & -z \\ x & -y & z\end{array}\right]$ satisfy the equation $\mathrm{A}^{\prime} \mathrm{A}=\mathrm{I}$.
View full solution →If $A=\left[\begin{array}{cc}0 & -\tan \frac{\alpha}{2} \\ \tan \frac{\alpha}{2} & 0\end{array}\right]$ and I is the identity matrix of order 2 , show that $I+A=(I-A)\left[\begin{array}{cc}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]$
View full solution →If $A=\left[\begin{array}{lll}1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3\end{array}\right]$, prove that $\mathrm{A}^3-6 \mathrm{~A}^2+7 \mathrm{~A}+2 \mathrm{I}=0$.
View full solution →If A = $\left[\begin{array}{lll} {3} & {\sqrt{3}} & {2} \\ {4} & {2} & {0} \end{array}\right] \text { and } B=\left[\begin{array}{rrr} {2} & {-1} & {2} \\ {1} & {2} & {4} \end{array}\right]$ verify that
View full solution →- (A′)′ = A
- (A + B)′ = A′ + B′
- (kB)′ = kB′, where k is any constant.
If A = $\left[\begin{array}{ccc} {1} & {1} & {-1} \\ {2} & {0} & {3} \\ {3} & {-1} & {2} \end{array}\right], B=\left[\begin{array}{cc} {1} & {3} \\ {0} & {2} \\ {-1} & {4} \end{array}\right]$ and C = $\left[\begin{array}{cccc} {1} & {2} & {3} & {-4} \\ {2} & {0} & {-2} & {1} \end{array}\right]$ find A(BC), (AB)C and show that (AB)C = A(BC).
View full solution →On her birthday, Seema decided to donate some money to the children of an orphanage home. If there were $8$ children less, everyone would have got $₹10$ more. However, if there were $16$ children more, everyone would have got $₹10$ less. Let the number of children be $\mathrm{x}$ and the amount distributed by Seema for one child be $\mathrm{y} \ ($in $₹)$.
$(i)$ Represent given information in matrix algebra.
$(ii)$ Find the adjoint of Matrix containing information about of number of children and amount she paid?
$(iii)$ Find the number of children who were given some money by Seema?
OR
How much amount does Seema spend in distributing the money to all the students of the Orphanage?
View full solution →$(i)$ Represent given information in matrix algebra.
$(ii)$ Find the adjoint of Matrix containing information about of number of children and amount she paid?
$(iii)$ Find the number of children who were given some money by Seema?
OR
How much amount does Seema spend in distributing the money to all the students of the Orphanage?
A trust fund has $₹ 35000$ that must be invested in two different types of bonds, say $\mathrm{X}$ and $\mathrm{Y}$. The first bond pays $10 \%$ interest p.a. which will be given to an old age home and second one pays $8 \%$ interest p.a. which will be given to WWA (Women Welfare Association). Let A be a $1 \times 2$ matrix and B be a $2 \times 1$ matrix, representing the investment and interest rate on each bond respectively.
View full solution →
(i) Represent the given information in matrix algebra.
(ii) If ₹ 15000 is invested in bond $\mathrm{X}$, then find total amount of interest received on both bonds?
(iii) If the trust fund obtains an annual total interest of ₹ 3200 , then find the investment in two bonds.
OR
If the amount of interest given to old age home is ₹500, then find the amount of investment in bond Y.
Three car dealers, say A, B and C, deals in three types of cars, namely Hatchback cars, Sedan cars, SUV cars. The sales figure of 2019 and 2020 showed that dealer A sold 120 Hatchback, 50 Sedan, 10 SUV cars in 2019 and 300 Hatchback, 150 Sedan, 20 SUV cars in 2020; dealer B sold 100 Hatchback, 30 Sedan, 5 SUV cars in 2019 and 200 Hatchback, 50 Sedan, 6 SUV cars in 2020; dealer C sold 90 Hatchback, 40 Sedan, 2 SUV cars in 2019 and 100 Hatchback, 60 Sedan, 5 SUV cars in 2020.
(i) Write the matrix summarizing sales data of 2019 and 2020.
(ii) Find the matrix summarizing sales data of 2020.
(iii) Find the total number of cars sold in two given years, by each dealer?
OR
If each dealer receives a profit of ₹ 50000 on sale of a Hatchback, ₹100000 on sale of a Sedan and ₹200000 on sale of an SUV, then find the amount of profit received in the year 2020 by each dealer.
Three friends Ravi, Raju and Rohit were doing buying and selling of stationery items in a market. The price of per dozen of pen, notebooks and toys are Rupees $\mathrm{x}, \mathrm{y}$ and $\mathrm{z}$ respectively.Ravi purchases $4$ dozen of notebooks and sells $2$ dozen of pens and $5$ dozen of toys. Raju purchases $2$ dozen of toy and sells $3$ dozen of pens and $1$ dozen of notebooks. Rohit purchases one dozen of pens and sells $3$ dozen of notebooks and one dozen of toys.
In the process, Ravi, Raju and Rohit earn $₹\ 1500, ₹\ 10$0 and $₹ \ 400$ respectively.
$(i)$ Write the above information in terms of matrix Algebra.
$(ii)$ What is the total price of one dozen of pens and one dozen of notebooks?
$(iii)$ What is the sale amount of Ravi?
$OR$
What is the amount of purchases and sales made by all three friends?
View full solution →In the process, Ravi, Raju and Rohit earn $₹\ 1500, ₹\ 10$0 and $₹ \ 400$ respectively.
$(i)$ Write the above information in terms of matrix Algebra.
$(ii)$ What is the total price of one dozen of pens and one dozen of notebooks?
$(iii)$ What is the sale amount of Ravi?
$OR$
What is the amount of purchases and sales made by all three friends?
The nut and bolt manufacturing business has gained popularity due to the rapid Industrialization and introduction of the Capital-Intensive Techniques in the Industries that are used as the Industrial fasteners to connect various machines and structures. Mr. Suresh is in Manufacturing business of Nuts and bolts. He produces three types of bolts, $\mathrm{x}, \mathrm{y}$, and $\mathrm{z}$ which he sells in two markets. Annual sales (in ₹) indicated below:
View full solution →
(i) If unit sales prices of $x, y$ and $z$ are $₹ 2.50$, ₹ 1.50 and $₹ 1.00$ respectively, then find the total revenue collected from Market-I \&II.
(ii) If the unit costs of the above three commodities are ₹2.00, ₹ 1.00 and 50 paise respectively, then find the cost price in Market I and Market II.
(iii) If the unit costs of the above three commodities are ₹2.00, ₹1.00 and 50 paise respectively, then find gross profit from both the markets.
OR
If matrix $\mathrm{A}=\left[a_{i j}\right]_{2 \times 2}$ where $\mathrm{a}_{\mathrm{ij}}=1$, if $\mathrm{i} \neq \mathrm{j}$ and $\mathrm{a}_{\mathrm{ij}}=0$, if $\mathrm{i}=\mathrm{j}$ then find $\mathrm{A}^2$.
Fill in the blank.
A matrix which is not a square matrix is called a _________ matrix.
A matrix which is not a square matrix is called a _________ matrix.
Fill in the blank.
If A and B are symmetric matrices of same order, then AB is symmetric if and only if _________.
If A and B are symmetric matrices of same order, then AB is symmetric if and only if _________.
Fill in the blank.
If A and B are symmetric matrices, then:
If A and B are symmetric matrices, then:
- AB – BA is a _________.
- BA – 2AB is a _________.
Fill in the blank.
If A is a symmetric matrix, then $A^3$ is a _________ matrix.
View full solution →If A is a symmetric matrix, then $A^3$ is a _________ matrix.
Fill in the blank.
_________ matrix is both symmetric and skew symmetric matrix.
_________ matrix is both symmetric and skew symmetric matrix.
Which of the following statements are True or False.
If A, B and C are square matrices of same order, then AB = AC always implies that B = C.
If A, B and C are square matrices of same order, then AB = AC always implies that B = C.
Which of the following statements are True or False.
If A and B are two square matrices of the same order, then AB = BA.
If A and B are two square matrices of the same order, then AB = BA.
Which of the following statements are True or False.
If A and B are two square matrices of the same order, then A + B = B + A.
If A and B are two square matrices of the same order, then A + B = B + A.
Which of the following statements are True or False.
Two matrices are equal if they have same number of rows and same number of columns.
Two matrices are equal if they have same number of rows and same number of columns.
Which of the following statements are True or False.If $\text{A}=\begin{bmatrix}2&3&-1\\1&4&2\end{bmatrix}$ and $\text{B}=\begin{bmatrix}2&3\\4&5\\2&1\end{bmatrix},$ then AB and BA are defined and equal.
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