In a third-order matrix A, a_{ij} denotes the | vedclass

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

Question

(A) Given the conditions for the elements of the $3 	imes 3$ matrix $A$:$a_{ij} = 0$ if $i = j$$a_{ij} = 1$ if $i > j$$a_{ij} = -1$ if $i < j$Constru

Vedclass · Accepted Answer

skew-symmetric

Vedclass · Answer

(A) Given the conditions for the elements of the $3 	imes 3$ matrix $A$:$a_{ij} = 0$ if $i = j$$a_{ij} = 1$ if $i > j$$a_{ij} = -1$ if $i Constructing the matrix $A$:$A = \begin{bmatrix} 0 & -1 & -1 \ 1 & 0 & -1 \ 1 & 1 & 0 \end{bmatrix}$Now, find the transpose $A^T$:$A^T = \begin{bmatrix} 0 & 1 & 1 \ -1 & 0 & 1 \ -1 & -1 & 0 \end{bmatrix} = -A$Since $A^T = -A$, the matrix $A$ is a skew-symmetric matrix.Now, calculate the determinant $|A|$:$|A| = 0(0 - (-1)) - (-1)(0 - (-1)) + (-1)(1 - 0)$$|A| = 0 + 1(1) - 1(1) = 1 - 1 = 0$Since the determinant $|A| = 0$, the matrix is singular and therefore not invertible.

In a third-order matrix $A$, $a_{ij}$ denotes the element in the $i$-th row and $j$-th column. If $a_{ij} = 0$ for $i = j$, $1$ for $i > j$, and $-1$ for $i < j$, then the matrix is:

Similar Questions

If $R(t) = \begin{bmatrix} \cos t & \sin t \\ -\sin t & \cos t \end{bmatrix}$,then $R(s) \cdot R(t) = $

Let $I$ denote the $3 \times 3$ identity matrix and $P$ be a matrix obtained by rearranging the columns of $I$. Then,

For matrices $X$ and $Y$,if $X+Y = \begin{bmatrix} 7 & 0 \\ 2 & 5 \end{bmatrix}$ and $X-Y = \begin{bmatrix} 3 & 0 \\ 0 & 3 \end{bmatrix}$,then $2X =$ . . . . . .

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

If $A+2B = \begin{bmatrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{bmatrix}$ and $2A-B = \begin{bmatrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2 \end{bmatrix}$, then $\operatorname{tr}(A)-\operatorname{tr}(B) =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module