Adjoint and Inverse of a Matrix - Uttarakhand Board (UBSE) STD 12 Science Maths Questions

Q 1M.C.Q (1 Marks)1 Mark

If $A$ is a matrix of order $3$ and $|A| = 8$, then $\text{|adj A| =}$

A
$1$
B
$2$
C
$2^3$
✓
$2^6$

Answer: D.

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Q 2M.C.Q (1 Marks)1 Mark

If A is a singular matrix, then adj A is:

A
Non-singular.
✓
Singular.
C
Symmetric.
D
Not defined.

Answer: B.

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Q 3M.C.Q (1 Marks)1 Mark

For non$-$singular square matrix $A, B$ and $C$ of the same order $(AB^{-1} C) =$

A
$A^{-1} BC^{-1}$
B
$C^{-1} B^{-1} A^{-1}$
C
$CBA^{-1}$
✓
$C^{-1} BA^{-1}$

Answer: D.

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Q 4M.C.Q (1 Marks)1 Mark

Let $\text{A}=\begin{bmatrix} 1 & 2 \\ 3 & -5 \end{bmatrix}$ and $B=\begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}$ and $X$ be a matrix such that $A = BX,$ then $X$ is equal to:

✓
$\frac{1}{2}\begin{bmatrix} 2 & 4 \\ 3 & -5 \end{bmatrix}$
B
$\frac{1}{2}\begin{bmatrix} -2 & 4 \\ 3 & 5 \end{bmatrix}$
C
$\begin{bmatrix} 2 & 4 \\ 3 & -5 \end{bmatrix}$
D
None of these.

Answer: A.

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Q 5M.C.Q (1 Marks)1 Mark

Let $\text{A}=\begin{bmatrix} 2 & 3 \\ 5 & -2 \end{bmatrix}$ be such that $A^{-1} = kA$, then $k$ equals:

A
$19$
✓
$\frac{1}{19}$
C
$-19$
D
$-\frac{1}{19}$

Answer: B.

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Q 62 Marks Questions2 Marks

If A is a square matrix of order $3$ such that $|adj\ A| = 64$, find $|A|$.

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Q 72 Marks Questions2 Marks

If $\text{A}=\begin{bmatrix} 3 & 1 \\ 2 & -3 \end{bmatrix},$ then find |adj A|.

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Q 82 Marks Questions2 Marks

Write the adjoint of the matrix $\text{A}=\begin{bmatrix} -3 & 4 \\ 7 & -2 \end{bmatrix}$.

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Q 92 Marks Questions2 Marks

If $A$ is a non-singular symmetric matrix, write whether $A^{-1}$ is symmetric or skew-symmetric.

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Q 102 Marks Questions2 Marks

If A is a square matrix of order $3$ such that $|A| = 5$, write the value of $|adj A|$.

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Q 113 Marks Question3 Marks

If $\text{adj A}=\begin{bmatrix} 2 & 3 \\ 4 & -1 \end{bmatrix} \text{and B}=\begin{bmatrix} 1 & -2 \\ -3 & 1 \end{bmatrix},$ find adj AB.

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Q 123 Marks Question3 Marks

Find the adjoint of the following matrices:$\begin{bmatrix}-3 & 5 \\ 2 & 4 \end{bmatrix}$
Verify that (adjoint A) A = |A|I = A (adjoint A) for the above matrices.

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Q 133 Marks Question3 Marks

Find the inverse of the following matrices:$\begin{bmatrix}\cos\theta & \sin\theta \\-\sin\theta & \cos\theta \end{bmatrix}$

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Q 143 Marks Question3 Marks

Find the inverse of the following matrices:$\begin{bmatrix}2 & 5 \\ -3 & 1 \end{bmatrix}$

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Q 153 Marks Question3 Marks

Find the inverse of the following matrices:$\begin{bmatrix} \text{a} & \text{b} \\ \text{c} & \frac{1+\text{bc}}{\text{a}} \end{bmatrix}$

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Q 165 Marks Questions5 Marks

Find the matrix X for which:$\begin{bmatrix}3 & 2 \\ 7 & 5 \end{bmatrix}\text{X}\begin{bmatrix} -1 & 1 \\ -2 & 1 \end{bmatrix}=\begin{bmatrix} 2 & -1 \\ 0 & 4 \end{bmatrix}$

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Q 175 Marks Questions5 Marks

Compute the adjoint of the following matrices:$\begin{bmatrix}2 & 0 & -1 \\5 & 1 & 0 \\ 1 & 1 & 3 \end{bmatrix}$
Verify that (adj A)A = |A| I = A (adj A) for the above matrices.

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Q 185 Marks Questions5 Marks

Compute the adjoint of the following matrices:$\begin{bmatrix}2 & -1 & 3 \\4 & 2 & 5 \\ 0 & 4 & -1 \end{bmatrix}$
Verify that (adj A)A = |A|I = A (adj A) for the above matrices.

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Q 195 Marks Questions5 Marks

If $\text{A}=\begin{bmatrix}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{bmatrix},$ find $A^{-1}$ and show that $\text{A}^{-1}=\frac{1}{2}(\text{A}^2-3\text{I}).$

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Q 205 Marks Questions5 Marks

For the following pairs of matrices verify that $(AB)^{-1} = B^{-1} A^{-1}:$
$\text{A}=\begin{bmatrix}2 & 1 \\5 & 3 \end{bmatrix}\text{ and B}=\begin{bmatrix}4 & 5 \\3 & 4 \end{bmatrix}$

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Adjoint and Inverse of a Matrix Maths - Adjoint and Inverse of a Matrix

Adjoint and Inverse of a Matrix question types

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