For any $2 \times 2$ matrix $P$, which of the following matrices can be $Q$ such that $P Q=Q P$ ?
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Matrices question types
242 questions across 9 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
242
Questions
9
Question groups
5
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01
M.C.Q (1 Marks)
80 Q→02Assertion (A) & Reason (B) MCQ
11 Q→031 Marks Question
32 Q→042 Marks Questions
53 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 $A=\left[\begin{array}{lll}1 & -1 & 1 \\ 1 & -1 & 1 \\ 1 & -1 & 1\end{array}\right]$, then $A^5-A^4-A^3+A^2$ is equal to
View full solution →If order of matrix $A$ is $2 \times 3$, of matrix $B$ is $3 \times 2$, and of matrix $C$ is $3 \times 3$, then which one of the following is not defined?
View full solution →Given that $A=\left[\begin{array}{cc}\alpha & \beta \\ \gamma & -\alpha\end{array}\right]$ and $A^2=31$, then
View full solution →If $A=\left[\begin{array}{rr}\cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha\end{array}\right]$ and $A+A^{\prime}=I$, then the value of $\alpha$ is
View full solution →Assertion (A): For any symmetric matrix A, B'AB is a skew-symmetric matrix.
Reason (R): A square matrix P is skew-symmetric if P'$P^{\prime}=-P$.
View full solution →Reason (R): A square matrix P is skew-symmetric if P'$P^{\prime}=-P$.
Assertion $(A) : A=\left[\begin{array}{ll}2 & 3 \\ 1 & 4\end{array}\right], B=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, then $(A+B)^2=A^2+B^2+2 A B$.
Reason $(R)$: For the matrices $A$ and $B$ given in assertion, $A B=B A$.
View full solution →Reason $(R)$: For the matrices $A$ and $B$ given in assertion, $A B=B A$.
Assertion $(A)$ : If $\left[\begin{array}{ll}x & 1\end{array}\right]\left[\begin{array}{cc}1 & 0 \\ -2 & 3\end{array}\right]\left[\begin{array}{c}x \\ -5\end{array}\right]=0$, then value of $x$ is either $-3$ or $5$ .
Reason $(R)$ : Two matrices $\left(\begin{array}{ll}x & y \\ u & v\end{array}\right)$ and $\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)$ are equal if and only if their corresponding entries are equal.
View full solution →Reason $(R)$ : Two matrices $\left(\begin{array}{ll}x & y \\ u & v\end{array}\right)$ and $\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)$ are equal if and only if their corresponding entries are equal.
Assertion (A): The matrix $A=\left(\begin{array}{ccc}0 & a & b \\ -a & 0 & c \\ -b & -c & 0\end{array}\right)$ is a skew-symmetric matrix.
Reason (R) : A square matrix $A=\left(a_{i j}\right)$ of order $m$ is said to be skew-symmetric if $A^T=-A$.
View full solution →Reason (R) : A square matrix $A=\left(a_{i j}\right)$ of order $m$ is said to be skew-symmetric if $A^T=-A$.
Assertion $(A)$ : If $A=\frac{1}{3}\left[\begin{array}{ccc}1 & -2 & 2 \\ -2 & 1 & 2 \\ -2 & -2 & -1\end{array}\right]$, then $A\left(A^T\right)=I$
Reason $(R)$ : For any square matrix $A,\left(A^T\right)^T=A$
View full solution →Reason $(R)$ : For any square matrix $A,\left(A^T\right)^T=A$
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
View full solution →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?
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 $\mathrm{A}^2$.
Three schools A, B and C organized a mela for collecting funds for helping the rehabilitation of flood victims. They sold handmade fans, mats, and plates from recycled material at a cost of ₹ 25 , ₹ 100 and ₹ 50 each. The number of articles sold by school A, B, C are given below.
View full solution →
(i) Represent the sale of handmade fans, mats and plates by three schools A, B and C and the sale prices (in ₹) of given products per unit, in matrix form.
(ii) Find the funds collected by school A, B and C by selling the given articles.
(iii) If they increase the cost price of each unit by $20 \%$, then write the matrix representing new price.
OR
Find the total funds collected for the required purpose after $20 \%$ hike in price.
Read the following passage and answer the questions given below.
View full solution →
In an elliptical sport field the authority wants to design a rectangular soccer field with the maximum possible area. The sport field is given by the graph of $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
(i) If the length and the breadth of the rectangular field be $2 x$ and $2 y$ respectively, then find the area function in terms of $x$.
(ii) Find the critical point of the function.
(iii) Use First derivative Test to find the length $2 x$ and width $2 y$ of the soccer field (in terms of $a$ and b) that maximize its area.
OR
(iii) Use Second Derivative Test to find the length $2 x$ and width $2 y$ of the soccer field (in terms of $a$ and $b$ ) that maximize its area.
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.
Sum of two skew symmetric matrices is always _________ matrix.
Sum of two skew symmetric matrices is always _________ matrix.
Fill in the blank.
If A is skew symmetric, then kA is a _________. (k is any scalar)
If A is skew symmetric, then kA is a _________. (k is any scalar)
Fill in the blank.
Matrix multiplication is _________ over addition.
Matrix multiplication is _________ over addition.
Fill in the blank.
If $A$ is a skew symmetric matrix, then $A^2$ is a _________.
View full solution →If $A$ is a skew symmetric matrix, then $A^2$ is a _________.
Which of the following statements are True or False.
Matrix addition is associative as well as commutative.
Matrix addition is associative as well as commutative.
Which of the following statements are True or False.
If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.
If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.
Which of the following statements are True or False.
Transpose of a column matrix is a column matrix.
Transpose of a column matrix is a column matrix.
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.
Matrices of any order can be added.
Matrices of any order can be added.
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