Let $\left|\begin{array}{ccc}6i& -3i& 1\\ 4& 3i& -1\\ 20& 3& i\end{array}\right|=x+iy$, then

Important Questions on Determinants

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 52

Suppose $D=\left|\begin{array}{lll}{a}_1& b_1& c_1\\ a_2& b_2& c_2\\ a_3& b_3& c_3\end{array}\right|$ and $D^{\text{'}}=\left|\begin{array}{lll}{a}_1+p{b}_1& b_1+q{c}_1& c_1+r{a}_1\\ a_2+p{b}_2& b_2+q{c}_2& c_2+r{a}_2\\ a_3+p{b}_3& b_3+q{c}_3& c_3+r{a}_3\end{array}\right|$, then

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 53

A root of the equation $\left|\begin{array}{ccc}3-x& -6& 3\\ -6& 3-x& 3\\ 3& 3& -6-x\end{array}\right|=0 \text{is}$

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 54

$\left|\begin{array}{lll}bc& b{c}^{\text{'}}+b^{\text{'}}c& b^{\text{'}}{c}^{\text{'}}\\ ca& c{a}^{\text{'}}+c^{\text{'}}a& c^{\text{'}}{a}^{\text{'}}\\ ab& a{b}^{\text{'}}+a^{\text{'}}b& a^{\text{'}}{b}^{\text{'}}\end{array}\right|$ is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 56

If $A$ is a square matrix of order $3$ and $det\left(A\right)=8$ then$det\left(adj\left(adj\left(A^2\right)\right)\right)$ is equal to $2^{\lambda }$, then $\lambda$ is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 58

If $A=\left[\begin{array}{ccc}0& 0& -1\\ 0& -1& 0\\ -1& 0& 0\end{array}\right]$ then $\mathrm{tr}\left(adj{A}^{50}\right)+\mathrm{tr}\left(A^{51}\right)+3\mathrm{tr}\left(A^{-1}\right)+5\left(tr\left({\left(A^2\right)}^{-1}\right)\right)$ is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 59

$A$ and $B$ are two non-singular matrices such that $A^6=I$ and $A{B}^2=BA\left(B\ne I\right)$, then find the value of $K$ so that $B^K=I$ is

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 60

If $A$ is an idempotent matrix satisfying ${\left(I-\frac{2}{5}A\right)}^{-1}=I-\alpha A$, then $\alpha$ is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 20 - Determinants>Assignment>Q 1

If $\Delta \left(n\right)=\left|\begin{array}{ccc}{x}^n& \sin x& \cos x\\ n!& \sin \frac{n\mathrm{\pi }}{2}& \cos \frac{n\mathrm{\pi }}{2}\\ \alpha & {\alpha }^2& {\alpha }^3\end{array}\right|$, then the value of $x=0$ is,