If A=left[begin{array}{lll}9 & 3 & 0 1 & 5 & | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) First, we calculate $AA^T$: $AA^T = \left[\begin{array}{lll}9 & 3 & 0 \ 1 & 5 & 8 \ 7 & 6 & 2\end{array}ight] \left[\begin{array}{lll}9 & 1 &

Vedclass · Accepted Answer

$35$

Vedclass · Answer

(A) First, we calculate $AA^T$: $AA^T = \left[\begin{array}{lll}9 & 3 & 0 \ 1 & 5 & 8 \ 7 & 6 & 2\end{array}ight] \left[\begin{array}{lll}9 & 1 & 7 \ 3 & 5 & 6 \ 0 & 8 & 2\end{array}ight] = \left[\begin{array}{lll}90 & 24 & 81 \ 24 & 90 & 53 \ 81 & 53 & 89\end{array}ight]$ Next, we calculate $A^2$: $A^2 = \left[\begin{array}{lll}9 & 3 & 0 \ 1 & 5 & 8 \ 7 & 6 & 2\end{array}ight] \left[\begin{array}{lll}9 & 3 & 0 \ 1 & 5 & 8 \ 7 & 6 & 2\end{array}ight] = \left[\begin{array}{lll}84 & 42 & 24 \ 70 & 76 & 56 \ 83 & 63 & 52\end{array}ight]$ Now, find $AA^T - A^2$: $AA^T - A^2 = \left[\begin{array}{ccc}90-84 & 24-42 & 81-24 \ 24-70 & 90-76 & 53-56 \ 81-83 & 53-63 & 89-52\end{array}ight] = \left[\begin{array}{ccc}6 & -18 & 57 \ -46 & 14 & -3 \ -2 & -10 & 37\end{array}ight]$ The sum of all elements $a_{ij}$ is: $\sum a_{ij} = 6 - 18 + 57 - 46 + 14 - 3 - 2 - 10 + 37 = 35$.

If $A=\left[\begin{array}{lll}9 & 3 & 0 \\ 1 & 5 & 8 \\ 7 & 6 & 2\end{array}\right]$ and $AA^T-A^2=\left[\begin{array}{lll}a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33}\end{array}\right]$, then $\sum_{\substack{1 \leq i \leq 3 \\ 1 \leq j \leq 3}} a_{i j}=$

Similar Questions

If $\begin{bmatrix} 1 & x & 1 \end{bmatrix} \begin{bmatrix} 1 & 3 & 2 \\ 0 & 5 & 1 \\ 0 & 3 & 2 \end{bmatrix} \begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix} = 0$,then $2x + 9 =$ . . . . . .

If $A = \begin{bmatrix} a & b \\ b & a \end{bmatrix}$ and $A^2 = \begin{bmatrix} \alpha & \beta \\ \beta & \alpha \end{bmatrix}$,then:

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$ and $A^2 - 5A = kI$,then $k =$ . . . . . .

If $A$ and $B$ are square matrices of order $2$,then $(A + B)^2 = $

If $ A=\left[\begin{array}{cc}0 & 1 \\ 1 & 0\end{array}\right] $,then $ A^{2} $ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module