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Important Questions on Matrices and Determinants

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 28

Let $a_{ij}$ denote the element of the ${\mathrm{i}}^{th }$ row and $j^{th }$ column in a $3\times 3$ matrix and let $a_{ij}=-a_{jj}$ for every $i$ and $j$ then this matrix is an -

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 29

Let $A$ be an invertible matrix then which of the following is/are true :

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 30

If $A=\left[\begin{array}{ccc}1& 9& -7\\ i& {\omega }^n& 8\\ 1& 6& {\omega }^{2n}\end{array}\right]$  and $i=\sqrt{-1}$ is complex cube root of unity, then $tr\left(A\right)$ will be-

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 31

If $A=\left[\begin{array}{ll}a& b\\ c& d\end{array}\right]$ satisfies the equation $x^2+k=0$, then

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 32

If $A$ and $B$ are invertible matrices, which one of the following statement is/are correct -

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 33

Matrix $\left[\begin{array}{ccc}a& b& (a\alpha -b)\\ b& c& (b\alpha -c)\\ 2& 1& 0\end{array}\right]$ is non invertible if

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 34

Let $A^{-1}=\left[\begin{array}{ccc}1& -1& 2\\ -1& 2& 1\\ 2& 1& -1\end{array}\right]$, then -

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Beta Question Bank for Engineering: Mathematics>Chapter 10 - Matrices and Determinants>EXERCISE-2>Q 35

Let $A=\left[\begin{array}{ccc}0& \tan \theta & 2\\ -\tan \theta & 0& \sec \theta \\ -2& -\sec \theta & 0\end{array}\right]$, where $\theta \ne (2n+1)\frac{\pi }{2}$ & $B=\sum _{r=1}^5{A}^{(2r-1)}$ then which of following statement is correct