Sample QuestionsMatrices questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Given $A=\left[\begin{array}{lll}0 & 4 & 6 \\ 3 & 0 & 1\end{array}\right]\left[\begin{array}{cc}0 & 1 \\ -1 & 2 \\ -5 & -6\end{array}\right]$ Find if possible $A^2$
View full solution →If $A=\left[\begin{array}{cc}0 & 2 \\ 5 & -2\end{array}\right], B=\left[\begin{array}{cc}1 & -1 \\ 3 & 2\end{array}\right]$and $I$ is a unit matrix of order $2 \times 2$ findb $BA$
View full solution →If $A=\left[\begin{array}{cc}0 & 2 \\ 5 & -2\end{array}\right], B=\left[\begin{array}{cc}1 & -1 \\ 3 & 2\end{array}\right]$ and $I$ is a unit matrix of order $2 \times 2$ find $AB$
View full solution →Evaluate if possible $\left[\begin{array}{ll}6 & 4 \\ 3 & 1\end{array}\right][-1,3]$
View full solution →Evaluate if possible $\left[\begin{array}{cc}6 & 4 \\ 3 & -1\end{array}\right]\left[\begin{array}{c}-1 \\ 3\end{array}\right]$
View full solution →Given $\left[\begin{array}{cc}2 & 1 \\ -3 & 4\end{array}\right] X=\left[\begin{array}{l}7 \\ 6\end{array}\right]$ write the order of matrix $x$
View full solution →If $[x, y]\left[\begin{array}{l}x \\ y\end{array}\right]=[25]$ and $\left[\begin{array}{ll}-x & y\end{array}\right]\left[\begin{array}{c}2 x \\ y\end{array}\right]=[-2]$ find $x$ and $y$ if $x, y \in Z ($integer$)$
View full solution →Given $A=\left[\begin{array}{ccc}0 & 4 & 6 \\ 3 & 0 & -1\end{array}\right]$ and $B=\left[\begin{array}{cc}0 & 1 \\ -1 & 2 \\ -5 & -6\end{array}\right]$ find if possible $BA$
View full solution →Given $A=\left[\begin{array}{ccc}0 & 4 & 6 \\ 3 & 0 & -1\end{array}\right]$ and $B=\left[\begin{array}{cc}0 & 1 \\ -1 & 2 \\ -5 & -6\end{array}\right]$ find if possible $AB$
View full solution →Find $x$ and $y$ if $\left[\begin{array}{cc}x & 0 \\ -3 & 1\end{array}\right]\left[\begin{array}{ll}1 & 1 \\ 0 & y\end{array}\right]=\left[\begin{array}{cc}2 & 2 \\ -3 & -2\end{array}\right]$
View full solution →Find $x$ and $y$ if $\left[\begin{array}{ll}x & 3 x \\ y & 4 y\end{array}\right]\left[\begin{array}{l}2 \\ 1\end{array}\right]=\left[\begin{array}{c}5 \\ 12\end{array}\right]$
View full solution →If $A=\left[\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right]$ and $B=\left[\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right]$ Find $(AB).B$
View full solution →If $A=\left[\begin{array}{ll}1 & 2 \\ 2 & 1\end{array}\right]$ and $B=\left[\begin{array}{ll}2 & 1 \\ 1 & 2\end{array}\right]$ Find $A(B A)$
View full solution →If $\left[\begin{array}{ll}a & 3 \\ 4 & 1\end{array}\right]+\left[\begin{array}{cc}2 & b \\ 1 & -2\end{array}\right]-\left[\begin{array}{cc}1 & 1 \\ -2 & c\end{array}\right]=\left[\begin{array}{ll}5 & 0 \\ 7 & 3\end{array}\right],$ Find the values of $a, b$ and $c$
View full solution →Evaluate $\left[\begin{array}{cc}\cos 45^{\circ} & \sin 30^{\circ} \\ \sqrt{2} \cos 0^{\circ} & \sin 0^{\circ}\end{array}\right]\left[\begin{array}{ll}\sin 45^{\circ} & \cos 90^{\circ} \\ \sin 90^{\circ} & \cot 45^{\circ}\end{array}\right]$
View full solution →If $A=\left[\begin{array}{ll}0 & -1 \\ 4 & -3\end{array}\right], B =\left[\begin{array}{c}-5 \\ 6\end{array}\right]$ and $3 A \times M =2 B$; Find matrix $M$
View full solution →Given $\left[\begin{array}{cc}2 & 1 \\ -3 & 4\end{array}\right] x=\left[\begin{array}{l}7 \\ 6\end{array}\right]$ Write the matrix $x$
View full solution →Given matrix $B=\left[\begin{array}{ll}1 & 1 \\ 8 & 3\end{array}\right]$ Find the matrix $X$ if, $X=B^2-4 B$. Hence, solve for $a$ and $b$ given $X\left[\begin{array}{l}a \\ b\end{array}\right]=\left[\begin{array}{c}5 \\ 50\end{array}\right]$
View full solution →Given matrix $A =\left[\begin{array}{l}4 \sin 30^{\circ}, \cos 0^{\circ} \\ \cos 0^{\circ}, 4 \sin 30^{\circ}\end{array}\right]$ and $B=\left[\begin{array}{l}4 \\ 5\end{array}\right]$ If $AX = B$. Find the matrix $'X\ '$
View full solution →Let $A=\left[\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right], B=\left[\begin{array}{cc}2 & 3 \\ -1 & 0\end{array}\right]$. Find $A^2+A B+B^2$
View full solution →If $A =\left[\begin{array}{ll}1 & 3 \\ 3 & 4\end{array}\right] B =\left[\begin{array}{ll}-2 & 1 \\ -3 & 2\end{array}\right]$ and $A^2-5 B^2=5 C$ Find the matrix $C$ where $C$ is a $2$ by $2$ matrix.
View full solution →Given $A=\left[\begin{array}{cc}2 & 0 \\ -1 & 7\end{array}\right]$ and $1=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ and $A^2=9 A+m l$. Find $m$
View full solution →if $A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]$ and $I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$, find $A^2-5 A+7 I$
View full solution →Find $x$ and $y$, if $\left(\begin{array}{cc}3 & -2 \\ -1 & 4\end{array}\right)\left(\begin{array}{c}2 x \\ 1\end{array}\right)+2\left(\begin{array}{c}-4 \\ 5\end{array}\right)=4\left(\begin{array}{l}2 \\ y\end{array}\right)$
View full solution →If $A=\left[\begin{array}{cc}3 & a \\ -4 & 8\end{array}\right], B=\left[\begin{array}{cc}c & 4 \\ -3 & 0\end{array}\right], C=\left[\begin{array}{cc}-1 & 4 \\ 3 & b\end{array}\right]$ and $3 A -2 C =6 B$, find the values of $a, b, c$.
View full solution →State,Whether the following statements is true or false.A, B and C are matrices of order 2 x 2.
(A – B)² = A² – 2A. B + B²
State,Whether the following statements is true or false.A, B and C are matrices of order 2 x 2.
A² – B² = (A + B) (A – B)
State,Whether the following statements is true or false.A, B and C are matrices of order 2 x 2.
(A – B). C = A. C – B. C
State,Whether the following statements is true or false.A, B and C are matrices of order 2 x 2.
A. (B - C) = A. B - A. C
State,Whether the following statements is true or false.A, B and C are matrices of order 2 x 2.
(A + B). C = A. C + B. C
If $\left[\begin{array}{ll}2 & 0 \\ 0 & 4\end{array}\right]\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{c}2 \\ -8\end{array}\right]$, the value of $x$ and $y$ respectively are:
Answer: A.
View full solution →If matrix $A=\left[\begin{array}{ll}2 & 2 \\ 0 & 2\end{array}\right]$ and $A^2=\left[\begin{array}{ll}4 & x \\ 0 & 4\end{array}\right]$, then thevalue of $x$ is:
Answer: C.
View full solution →Which of the following is/are correct?
Statement (A): If $A=\left[\begin{array}{rr}3 & 1 \\ -1 & 2\end{array}\right]$, then $A ^2=\left[\begin{array}{rr}8 & -5 \\ 5 & 3\end{array}\right]$
Statement (B): If $A=\left[\begin{array}{rr}3 & 1 \\ -1 & 2\end{array}\right], B=\left[\begin{array}{ll}5 & x \\ 1 & 0\end{array}\right]$ and $A^2=B$, then the value of $x$ is 5 .
Statement (C): For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix.
- A
- ✓
- C
- D
All A, B and C are correct
Answer: B.
View full solution →Which of the following is/are correct?
Statement (A): A row matrix has only one row and multiple columns.
Statement (B): A column matrix has only one column and multiple rows.
Statement (C): The addition of a row matrix with a column matrix is always possible.
- ✓
- B
- C
- D
All A, B and C are correct
Answer: A.
View full solution →Statement (A): Adding the null matrix $\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$ to any $2 \times 2$ matrix $\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$ will result in the original matrix $\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$.
Statement (B): Multiplying any $2 \times 2$ matrix by the identity matrix $\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$ will change thevalues of the elements in the original matrix.
Which of the statement is valid?
Answer: A.
View full solution →Assertion : If $A$ and $B$ are square matrices of order 2 , then $A B=B A$ is not always true.
Reason : Matrix multiplication is associative.
- A
Both assertion and reason are correct and reason is the correct explanation of assertion.
- ✓
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- D
Assertion is incorrect but reason is correct.
Answer: B.
View full solution →Assertion : If $\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right] X=\left[\begin{array}{l}2 \\ 1\end{array}\right]$, then the order of matrix $X$ is $1 \times 2$.
Reason : The product $A B$ of two matrices $A$ and $B$ is possible if number of columns in $A$ is equal to the number of rows in B. Also, the order of the product matrix $A B$ is number of rows in $A X$ number of columns in B.
- A
Both assertion and reason are correct and reason is the correct explanation of assertion.
- B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- ✓
Assertion is incorrect but reason is correct.
Answer: D.
View full solution →Assertion : $\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$ is a row matrix and [1 2 3] is a column matrix.
Reason: Matrix having only one row is called row matrix and matrix having only one column is called column matrix.
- A
Both assertion and reason are correct and reason is the correct explanation of assertion.
- B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- ✓
Assertion is incorrect but reason is correct.
Answer: D.
View full solution → Assertion : Let $A=\left[\begin{array}{ll}2 & 3 \\ 7 & 5\end{array}\right]$ and
$B =\left[\begin{array}{cc}m-n & 6 \\ 14 & m+n\end{array}\right]$ If $2 A= B$,
then $m=7$ and $n=3$.
Reason : Two equal matrices have the same order and their corresponding elements are also equal.
- ✓
Both assertion and reason are correct and reason is the correct explanation of assertion.
- B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- D
Assertion is incorrect but reason is correct.
Answer: A.
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