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 $A^{T} = A$ and $B^{T} = B$.We are given $X = AB + BA$ and $Y = AB - BA$.We need to find $(X

Vedclass · Accepted Answer

$-YX$

Vedclass · Answer

(C) Given that $A$ and $B$ are symmetric matrices,we have $A^{T} = A$ and $B^{T} = B$.We are given $X = AB + BA$ and $Y = AB - BA$.We need to find $(XY)^{T}$.Using the property of transpose $(XY)^{T} = Y^{T} X^{T}$.First,let us find $X^{T}$ and $Y^{T}$:$X^{T} = (AB + BA)^{T} = (AB)^{T} + (BA)^{T} = B^{T}A^{T} + A^{T}B^{T} = BA + AB = X$.$Y^{T} = (AB - BA)^{T} = (AB)^{T} - (BA)^{T} = B^{T}A^{T} - A^{T}B^{T} = BA - AB = -(AB - BA) = -Y$.Now,$(XY)^{T} = Y^{T} X^{T}$.Substituting the values of $Y^{T}$ and $X^{T}$,we get:$(XY)^{T} = (-Y)(X) = -YX$.

If $A$ and $B$ are symmetric matrices of the same order such that $AB+BA=X$ and $AB-BA=Y$,then $(XY)^{T}=$

Similar Questions

If $A^{\prime}=\begin{bmatrix} 3 & 4 \\ -1 & 2 \\ 0 & 1 \end{bmatrix}$ and $B=\begin{bmatrix} -1 & 2 & 1 \\ 1 & 2 & 3 \end{bmatrix}$,then verify that $(A-B)^{\prime}=A^{\prime}-B^{\prime}$.

For the matrix $A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix}$,verify that $(A - A^{\prime})$ is a skew-symmetric matrix.

If $P$ and $Q$ are symmetric matrices of the same order,then $PQ - QP$ is

If $A$ is a square matrix,then which of the following matrices is not symmetric?

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module