ExamGOAL
Books
PreviousNext
67
MCQ (Single Correct Answer)

On using elementary row operation $R_1 \rightarrow R_1-3 R_2$ in the following matrix equation $\left[\begin{array}{ll}4 & 2 \\ 3 & 3\end{array}\right]=\left[\begin{array}{ll}1 & 2 \\ 0 & 3\end{array}\right]\left[\begin{array}{ll}2 & 0 \\ 1 & 1\end{array}\right]$, we have

A
$\left[\begin{array}{rr}-5 & -7 \\ 3 & 3\end{array}\right]=\left[\begin{array}{cc}1 & -7 \\ 0 & 3\end{array}\right]\left[\begin{array}{ll}2 & 0 \\ 1 & 1\end{array}\right]$
B
$\left[\begin{array}{rr}-5 & -7 \\ 3 & 3\end{array}\right]=\left[\begin{array}{ll}1 & 2 \\ 0 & 3\end{array}\right]\left[\begin{array}{rr}-1 & -3 \\ 1 & 1\end{array}\right]$
C
$\left[\begin{array}{rr}-5 & -7 \\ 3 & 3\end{array}\right]=\left[\begin{array}{rr}1 & 2 \\ 1 & -7\end{array}\right]\left[\begin{array}{ll}2 & 0 \\ 1 & 1\end{array}\right]$
D
$\left[\begin{array}{rr}4 & 2 \\ -5 & -7\end{array}\right]=\left[\begin{array}{rr}1 & 2 \\ -3 & -3\end{array}\right]\left[\begin{array}{ll}2 & 0 \\ 1 & 1\end{array}\right]$
68

........... matrix is both symmetric and skew-symmetric matrix.

Explanation

Null matrix is both symmetric and skew-symmetric matrix.

69

Sum of two skew-symmetric matrices is always ........... matrix.

Explanation

Let $A$ is a given matrix, then $(-A)$ is a skew-symmetric matrix. Similarly, for a given matrix $-B$ is a skew-symmetric matrix. Hence, $-A-B=-(A+B) \Rightarrow$ sum of two skew-symmetric matrices is always skew-symmetric matrix.

70

The negative of a matrix is obtained by multiplying it by ............ .

Explanation

Let $A$ is a given matrix.

$\therefore \quad-A=-1[A]$

So, the negative of a matrix is obtained by multiplying it by $-1$.

71

The product of any matrix by the scalar ............. is the null matrix.

Explanation

The product of any matrix by the scalar 0 is the null matrix. i.e., $0 \cdot A=0$. [where, $A$ is any matrix]

PreviousNext