Let $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 1 \\ -2 & 0 \end{bmatrix}$. Match the matrix on the left column with the matrix on the right column. Then choose the correct option. Left column: (i) $A + A^T$; (ii) $(A + B)^T$; (iii) $(AB)^T$; (iv) $B + B^T$. Right column: (a) $\begin{bmatrix} -2 & -1 \\ -1 & 0 \end{bmatrix}$; (b) $\begin{bmatrix} 2 & 5 \\ 5 & 8 \end{bmatrix}$; (c) $\begin{bmatrix} 0 & 1 \\ 3 & 4 \end{bmatrix}$; (d) $\begin{bmatrix} -5 & -11 \\ 1 & 3 \end{bmatrix}$. (a) (i)-(a), (ii)-(c), (iii)-(d), (iv)-(b) (b) (i)-(b), (ii)-(c), (iii)-(a), (iv)-(d) (c) (i)-(b), (ii)-(c), (iii)-(d), (iv)-(a) (d) (i)-(b), (ii)-(d), (iii)-(c), (iv)-(a)

> > [!TLDR] > Compute each of the four matrices and match; the correct assignment is (i)-(b), (ii)-(c), (iii)-(d), (iv)-(a). > > Matrix operations and the transpose rules $(A+B)^T=A^T+B^T$, $(AB)^T=B^TA^T$ are exactly the CBSE/NCERT Class 12 matrices topics tested here. > > (i) $A+A^T = \begin{bmatrix}1&2\\3&4\end{bmatrix}+\begin{bmatrix}1&3\\2&4\end{bmatrix} = \begin{bmatrix}2&5\\5&8\end{bmatrix}$ — matches (b). > > (ii) $A+B = \begin{bmatrix}0&3\\1&4\end{bmatrix}$, so $(A+B)^T = \begin{bmatrix}0&1\\3&4\end{bmatrix}$ — matches (c). > …

Let A = 1 2 \3 4 and B = -1 1 \-2 0 . Match the matrix on the left column with the matrix on the right column.

Question 49 of 52

A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}

(i)

A + A^T

;

(ii)

(A + B)^T

;

(iii)

(AB)^T

;

(iv)

B + B^T

. Right column:

(a)

\begin{bmatrix} -2 & -1 \\ -1 & 0 \end{bmatrix}

;

(b)

\begin{bmatrix} 2 & 5 \\ 5 & 8 \end{bmatrix}

;

(c)

\begin{bmatrix} 0 & 1 \\ 3 & 4 \end{bmatrix}

;

(d)

\begin{bmatrix} -5 & -11 \\ 1 & 3 \end{bmatrix}

(a) (i)-(a), (ii)-(c), (iii)-(d), (iv)-(b)

(b) (i)-(b), (ii)-(c), (iii)-(a), (iv)-(d)

(d) (i)-(b), (ii)-(d), (iii)-(c), (iv)-(a)

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Compute each of the four matrices and match; the correct assignment is (i)-(b), (ii)-(c), (iii)-(d), (iv)-(a).

Matrix operations and the transpose rules $(A+B)^T=A^T+B^T$ , $(AB)^T=B^TA^T$ are exactly the CBSE/NCERT Class 12 matrices topics tested here.

$A+A^T = \begin{bmatrix}1&2\\3&4\end{bmatrix}+\begin{bmatrix}1&3\\2&4\end{bmatrix} = \begin{bmatrix}2&5\\5&8\end{bmatrix}$ — matches (b).
$A+B = \begin{bmatrix}0&3\\1&4\end{bmatrix}$ , so $(A+B)^T = \begin{bmatrix}0&1\\3&4\end{bmatrix}$ — matches (c). …

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Q.Let $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 1 \\ -2 & 0 \end{bmatrix}$ . Match the matrix on the left column with the matrix on the right column. Then choose the correct option. Left column:

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Q.Let $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$ and $B = \begin{bmatrix} -1 & 1 \\ -2 & 0 \end{bmatrix}$ . Match the matrix on the left column with the matrix on the right column. Then choose the correct option. Left column:

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