If A and B are two square matrices of the sam | vedclass

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

Question

(A) Given the equation: $(AB+BA)^{T}+(AB-BA)^{T}=2BA$ Using the property $(X+Y)^T = X^T + Y^T$, we get: $(AB)^T + (BA)^T + (AB)^T - (BA)^T = 2BA$ $2(A

Vedclass · Accepted Answer

$A$ and $B$ are both symmetric matrices but not skew-symmetric matrices

Vedclass · Answer

(A) Given the equation: $(AB+BA)^{T}+(AB-BA)^{T}=2BA$ Using the property $(X+Y)^T = X^T + Y^T$, we get: $(AB)^T + (BA)^T + (AB)^T - (BA)^T = 2BA$ $2(AB)^T = 2BA$ $(AB)^T = BA$ $B^T A^T = BA$ If $A$ and $B$ are symmetric, then $A^T = A$ and $B^T = B$. Substituting these, we get $BA = BA$, which is true. If $A$ and $B$ are skew-symmetric, then $A^T = -A$ and $B^T = -B$. Substituting these, we get $(-B)(-A) = BA$, which is $BA = BA$, which is also true. Thus, the condition holds if $A$ and $B$ are both symmetric or both skew-symmetric. Since the options provided are limited, the most appropriate conclusion based on the derivation is that the property holds for both cases.

If $A$ and $B$ are two square matrices of the same order and $(AB+BA)^{T}+(AB-BA)^{T}=2BA$, then:

Similar Questions

If $A, B, C$ are the angles of a triangle,then the value of the determinant $\left| \begin{array}{ccc} \sin 2A & \sin C & \sin B \\ \sin C & \sin 2B & \sin A \\ \sin B & \sin A & \sin 2C \end{array} \right|$ is

Let $\alpha$ and $\beta$ be real numbers. Consider a $3 \times 3$ matrix $A$ such that $A^2 = 3A + \alpha I$. If $A^4 = 21A + \beta I$,then:

Let $A$ and $B$ be two square matrices of order $3$ such that $|A|=3$ and $|B|=2$. Then $\left|A^{T} A(\operatorname{adj}(2A))^{-1}(\operatorname{adj}(4B))(\operatorname{adj}(AB))^{-1} AA^{T}\right|$ is equal to:

For a $3 \times 3$ matrix $A$,if $A(\operatorname{adj} A) = \begin{bmatrix} -10 & 0 & 0 \\ 0 & -10 & 2 \\ 0 & 0 & -10 \end{bmatrix}$,then the value of the determinant of $A$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module