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3 and 4 .Determinants and Matrices
easy
If $A$ is a square matrix for which ${a_{ij}} = {i^2} - {j^2}$, then $A$ is
A
Zero matrix
B
Unit matrix
C
Symmetric matrix
D
Skew symmetric matrix
Solution
(d) ${a_{ji}} = {i^2} – {j^2}$ is a square matrix.
For a skew symmetric matrix ${a_{ji}} = -{a_{ji}}$
$\Rightarrow$ ${a_{ij}} = {i^2} – {j^2}$ and ${a_{ji}} = {j^2} – {i^2}$
$\Rightarrow$ ${a_{ij}} + {a_{ji}} = 0$
$\Rightarrow \,{a_{ij}} = – {a_{ji}}$
Hence, $ {a_{ji}}$ is a skew symmetric matrix.
Standard 12
Mathematics
Similar Questions
Match the Statements / Expressions in Column $I$ with the Statements / Expressions in Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
| Column $I$ | Column $II$ |
| $(A)$ The minimum value of $\frac{x^2+2 x+4}{x+2}$ is | $(p)$ $0$ |
| $(B)$ Let $A$ and $B$ be $3 \times 3$ matrices of real numbers, where $A$ is symmetric, $B$ is skewsymmetric, and $(A+B)(A-B)=(A-B)(A+B)$. If $(A B)^t=(-1)^k A B$, where $(A B)^t$ is the transpose of the matrix $A B$, then the possible values of $k$ are | $(q)$ $1$ |
| $(C)$ Let $\mathrm{a}=\log _3 \log _3 2$. An integer $\mathrm{k}$ satisfying $1<2^{\left(-k+3^{-2}\right)}<2$, must be less than | $(r)$ $2$ |
| $(D)$ If $\sin \theta=\cos \phi$, then the possible values of $\frac{1}{\pi}\left(\theta \pm \phi-\frac{\pi}{2}\right)$ are | $(s)$ $3$ |
