If A and B are symmetric matrices of the same | vedclass

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

Question

(C) Given that $A$ and $B$ are symmetric matrices,we have:$A^{\prime} = A$ and $B^{\prime} = B$  .......... $(1)$Consider the transpose of the matrix

Vedclass · Accepted Answer

Skew-symmetric matrix

Vedclass · Answer

(C) Given that $A$ and $B$ are symmetric matrices,we have:$A^{\prime} = A$ and $B^{\prime} = B$  .......... $(1)$Consider the transpose of the matrix $(AB - BA)$:$(AB - BA)^{\prime} = (AB)^{\prime} - (BA)^{\prime}$Using the property $(XY)^{\prime} = Y^{\prime}X^{\prime}$,we get:$(AB - BA)^{\prime} = B^{\prime}A^{\prime} - A^{\prime}B^{\prime}$Substituting the values from $(1)$:$(AB - BA)^{\prime} = BA - AB$Factoring out the negative sign:$(AB - BA)^{\prime} = -(AB - BA)$Since the transpose of $(AB - BA)$ is equal to its negative,$(AB - BA)$ is a skew-symmetric matrix.

If $A$ and $B$ are symmetric matrices of the same order,then $AB - BA$ is a

Similar Questions

If $A = \begin{bmatrix} 1 & -2 \\ 3 & 0 \end{bmatrix}$,$B = \begin{bmatrix} -1 & 4 \\ 2 & 3 \end{bmatrix}$,$C = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$,then $5A - 3B - 2C = $

If $A = \begin{bmatrix} 0 & 3 \\ 0 & 0 \end{bmatrix}$ and $f(x) = x + x^2 + x^3 + \ldots + x^{2023}$,then $f(A) + I = $

If $A = \begin{bmatrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \end{bmatrix}$ and $B = \begin{bmatrix} -5 & 7 & 1 \\ 1 & -5 & 7 \\ 7 & 1 & -5 \end{bmatrix}$,then $AB$ is equal to

If $A = \begin{bmatrix} 1 & a \\ 0 & 1 \end{bmatrix}$,then $A^4$ is equal to

If $X = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix}$,then the value of $X^n$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module