If left{ begin{bmatrix} 3 & 1 & 2 8 & 9 & 5 | vedclass

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

Question

(A) Let $A = \begin{bmatrix} 3 & 1 & 2 \ 8 & 9 & 5 \ 1 & 1 & 3 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 & 3 \ 3 & 2 & 7 \ 3 & 7 & 9 \end{bmat

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) Let $A = \begin{bmatrix} 3 & 1 & 2 \ 8 & 9 & 5 \ 1 & 1 & 3 \end{bmatrix}$ and $B = \begin{bmatrix} 1 & 3 & 3 \ 3 & 2 & 7 \ 3 & 7 & 9 \end{bmatrix}$.Note that $A^T = \begin{bmatrix} 3 & 8 & 1 \ 1 & 9 & 1 \ 2 & 5 & 3 \end{bmatrix}$.The given expression is $X = (ABA^T)^2$.Since $B$ is a symmetric matrix $(B^T = B)$,the matrix $ABA^T$ is also symmetric because $(ABA^T)^T = (A^T)^T B^T A^T = ABA^T$.If a matrix $M$ is symmetric,then $M^2$ is also symmetric.Thus,$X = (ABA^T)^2$ is a symmetric matrix.For a symmetric matrix $X = \begin{bmatrix} a_1 & a_2 & a_3 \ b_1 & b_2 & b_3 \ c_1 & c_2 & c_3 \end{bmatrix}$,we have $a_2 = b_1$,$a_3 = c_1$,and $b_3 = c_2$.Therefore,$|a_2 - b_1| + |a_3 - c_1| + |b_3 - c_2| = |0| + |0| + |0| = 0$.

Similar Questions

Let $A = [a_{ij}]_{2 \times 2}$ where $a_{ij} \neq 0$ for all $i, j$ and $A^2 = I$. Let $a$ be the sum of all diagonal elements of $A$ and $b = |A|$. Then $3a^2 + 4b^2$ is equal to:

If $\begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix}$ is a skew-symmetric matrix and $b, c, f$ are non-zero real numbers, then $\frac{b}{c} = $

Let $S$ be the set containing all $3 \times 3$ matrices with entries from $\{-1, 0, 1\}$. The total number of matrices $A \in S$ such that the sum of all the diagonal elements of $A^{T}A$ is $6$ is:

Find $x,$ if $[x \ -5 \ -1]\begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix}\begin{bmatrix} x \\ 4 \\ 1 \end{bmatrix} = O$

Vedclass Test Series

Exam Paper Generator

Online Exam Module