Let A=bmatrix1 & 0 \\ -1 & 7bmatrix and B=bmatrix0 & 4 \\ -1 & 7bmatrix then Match List-I with List-II, List-I, List-II, Determinants, Value, (A) A^2, (I) 28, (B) AB^T, (II) 7, (C) adj A, (III) 16, (D) 2B, (IV) 49, Choose the correct answer from the options given below: Option 1: (A) - (I), (B) - (III), (C) - (II), (D) - (IV) Option 2: (A) - (IV), (B) - (II), (C) - (I), (D) - (III) Option 3: (A) - (II), (B) - (III), (C) - (I), (D) - (IV) Option 4: (A) - (IV), (B) - (I), (C) - (II), (D) - (III)

Answer: (A) - (IV), (B) - (I), (C) - (II), (D) - (III). Solution: A, = 7 and, B, = 0(7)-4(-1) = 4. (A), A^2, =, A, ^2 = 49. (B), AB^T, =, A, B, = 28. (C), adj A, =, A, ^(n-1) = 7. (D), 2B, = 2^2, B, = 16.

Algebra

Matrices & Determinants

Medium

core

Let $A=\begin{bmatrix}1 & 0 \\ -1 & 7\end{bmatrix}$ and $B=\begin{bmatrix}0 & 4 \\ -1 & 7\end{bmatrix}$ then

Match List-I with List-II

List-I List-II
Determinants Value
(A) $\left\vert A^{2} \right\vert$ (I) $28$
(B) $\left\vert AB^{T} \right\vert$ (II) $7$
(C) $\left\vert \text{adj } A \right\vert$ (III) $16$
(D) $\left\vert 2B \right\vert$ (IV) $49$

Choose the correct answer from the options given below:

List-I	List-II
Determinants	Value
(A) $\left\vert A^{2} \right\vert$	(I) $28$
(B) $\left\vert AB^{T} \right\vert$	(II) $7$
(C) $\left\vert \text{adj } A \right\vert$	(III) $16$
(D) $\left\vert 2B \right\vert$	(IV) $49$

(A) - (I), (B) - (III), (C) - (II), (D) - (IV)

(A) - (IV), (B) - (II), (C) - (I), (D) - (III)

(A) - (II), (B) - (III), (C) - (I), (D) - (IV)

(A) - (IV), (B) - (I), (C) - (II), (D) - (III)

✅ Correct Option: 4

$|A| = 7$ and $|B| = 0(7)-4(-1) = 4$ .

(A) $|A^2| = |A|^2 = 49$ .

(B) $|AB^T| = |A||B| = 28$ .

(D) $|2B| = 2^2|B| = 16$ .

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Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	$A = \begin{bmatrix}3 & 5\\ 5 & 2\end{bmatrix}$	I.	Scalar matrix
B.	$A = \begin{bmatrix}0 & -2\\ 2 & 0\end{bmatrix}$	II.	Upper triangular matrix
C.	$A = \begin{bmatrix}5 & 3\\ 0 & 4\end{bmatrix}$	III.	Symmetric matrix
D.	$A = \begin{bmatrix}3 & 0\\ 0 & 3\end{bmatrix}$	IV.	Skew symmetric matrix

Choose the correct answer from the options given below:

Solution

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