If the matrix left[begin{array}{rr}2 & 3 5 & | vedclass

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

Question

(D) Given,$C = \left[\begin{array}{rr}2 & 3 \ 5 & -1\end{array}ight] = A+B$. We know that any square matrix $C$ can be uniquely expressed as the su

Vedclass · Accepted Answer

$\left[\begin{array}{rr}0 & -1 \ 1 & 0\end{array}ight]$

Vedclass · Answer

(D) Given,$C = \left[\begin{array}{rr}2 & 3 \ 5 & -1\end{array}ight] = A+B$. We know that any square matrix $C$ can be uniquely expressed as the sum of a symmetric matrix $A$ and a skew-symmetric matrix $B$,where $A = \frac{1}{2}(C+C^T)$ and $B = \frac{1}{2}(C-C^T)$. First,find the transpose of $C$: $C^T = \left[\begin{array}{rr}2 & 5 \ 3 & -1\end{array}ight]$. Now,calculate $B = \frac{1}{2}(C-C^T)$: $B = \frac{1}{2} \left( \left[\begin{array}{rr}2 & 3 \ 5 & -1\end{array}ight] - \left[\begin{array}{rr}2 & 5 \ 3 & -1\end{array}ight] ight)$ $B = \frac{1}{2} \left[\begin{array}{rr}2-2 & 3-5 \ 5-3 & -1-(-1)\end{array}ight]$ $B = \frac{1}{2} \left[\begin{array}{rr}0 & -2 \ 2 & 0\end{array}ight]$ $B = \left[\begin{array}{rr}0 & -1 \ 1 & 0\end{array}ight]$.

If the matrix $\left[\begin{array}{rr}2 & 3 \\ 5 & -1\end{array}\right]=A+B$,where $A$ is symmetric and $B$ is skew-symmetric,then $B$ is equal to

Similar Questions

If $I$ is the identity matrix of order $2$ and $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$, then for $n \geq 1$, mathematical induction gives:

What must be the matrix $X$ if $2X + \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} = \begin{bmatrix} 3 & 8 \\ 7 & 2 \end{bmatrix}$?

If $A = \begin{bmatrix} 0 & 2 \\ 3 & -4 \end{bmatrix}$ and $hA = \begin{bmatrix} 0 & 3a \\ 2b & 24 \end{bmatrix}$, then the values of $h, a, b$ are respectively

If ${a_{ij}} = \frac{1}{2}(3i - 2j)$ and $A = {[{a_{ij}}]_{2 \times 2}}$,then $A$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module