If M and N are square matrices of order 3,the | vedclass

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

Question

(C) For two square matrices $M$ and $N$ of order $3$: $1$. The matrix $MN - NM$ is skew-symmetric if $M$ and $N$ are symmetric matrices,because $(MN -

Vedclass · Accepted Answer

For all symmetric matrices $M$ and $N$,matrix $MN$ is symmetric

Vedclass · Answer

(C) For two square matrices $M$ and $N$ of order $3$: $1$. The matrix $MN - NM$ is skew-symmetric if $M$ and $N$ are symmetric matrices,because $(MN - NM)^T = (MN)^T - (NM)^T = N^T M^T - M^T N^T = NM - MN = -(MN - NM)$. $2$. The matrix $N^T MN$ is symmetric or skew-symmetric according as $M$ is symmetric or skew-symmetric,because $(N^T MN)^T = N^T M^T (N^T)^T = N^T M^T N$. If $M^T = M$,then $(N^T MN)^T = N^T MN$ (symmetric). If $M^T = -M$,then $(N^T MN)^T = -N^T MN$ (skew-symmetric). $3$. The product of two symmetric matrices $MN$ is symmetric if and only if $MN = NM$. Since this is not true for all symmetric matrices,statement $(c)$ is false. $4$. For any two matrices $M$ and $N$,$	ext{adj}(MN)$ and $	ext{adj}(NM)$ are not necessarily equal. Thus,the statement that is not true is $(c)$.

If $M$ and $N$ are square matrices of order $3$,then which one of the following statements is not true?

Similar Questions

If $\begin{bmatrix} -1 & 2 & b \\ a & 5 & 6 \\ 3 & c & 7 \end{bmatrix}$ is a symmetric matrix,then $\begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix} =$

Let $A = \begin{bmatrix} m & n \\ p & q \end{bmatrix}$,$d = |A| \neq 0$ and $|A - d(\operatorname{Adj} A)| = 0$. Then:

If $A$ and $B$ are $3 \times 3$ order matrices and $|A|=5$,$|B|=3$,then $|3AB|=$ . . . . . . .

Let $A, B, C, D$ be square real matrices such that $C^T = DAB$,$D^T = ABC$,and $S = ABCD$. Then $S^2$ is equal to:

If $\Delta=\left|\begin{array}{lll}1 & 5 & 6 \\ 0 & 1 & 7 \\ 0 & 0 & 1\end{array}\right|$ and $\Delta^{\prime}=\left|\begin{array}{ccc}1 & 0 & 1 \\ 3 & 0 & 3 \\ 4 & 6 & 100\end{array}\right|$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module