# Matrices and Determinants · Mathematics · COMEDK

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COMEDK 2024 Evening Shift
$$\text { If } 3 A+4 B^t=\left(\begin{array}{ccc} 7 & -10 & 17 \\ 0 & 6 & 31 \end{array}\right) \text { and } 2 B-3 A^t=\left(\begin{array}{cc} -1 & ... COMEDK 2024 Evening Shift$$ \text { If } A=\left[\begin{array}{cc} 5 a & -b \\ 3 & 2 \end{array}\right] \text { and } A \operatorname{adj} A=A A^t \text {, then } 5 a+b \text ...
COMEDK 2024 Evening Shift
If the matrix $A$ is such that $$A\left(\begin{array}{cc}-1 & 2 \\ 3 & 1\end{array}\right)=\left(\begin{array}{cc}-4 & 1 \\ 7 & 7\end{array}\right)$$ ...
COMEDK 2024 Evening Shift
If $$A=\left[\begin{array}{ccc}0 & x & 16 \\ x & 5 & 7 \\ 0 & 9 & x\end{array}\right]$$ is a singular matrix then $$x$$ is equal to
COMEDK 2024 Morning Shift
$$\text { If } P=\left[\begin{array}{lll} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{array}\right] \text { is the adjoint of a } 3 \times 3 \text ... COMEDK 2024 Morning Shift If$$A=\left[\begin{array}{ccc}-1 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right]$$then the inverse of$$(A I)^t$$(where$$\mathrm{I}$$is an id... COMEDK 2024 Morning Shift$$ \text { If } x, y, z \text { are non zero real numbers, then inverse of matrix } A=\left[\begin{array}{lll} x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z \en...
COMEDK 2024 Morning Shift
$$\text { If the matrix } A=\left(\begin{array}{cc} 1 & -1 \\ -1 & 1 \end{array}\right) \text { then } A^{n+1}=$$
COMEDK 2024 Morning Shift
If $$\left[\begin{array}{lll} 1 & x & 1 \end{array}\right]\left[\begin{array}{ccc} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{array}\right]\left[\begi... COMEDK 2023 Morning Shift If$$A=\left[\begin{array}{ll}2 & 2 \\ 3 & 4\end{array}\right]$$, then$$A^{-1}$$equals to COMEDK 2023 Morning Shift If$$A$$is a matrix of order$$4 \operatorname{such}$$that$$A(\operatorname{adj} A)=10 \mathrm{~I}$$, then$$|\operatorname{adj} A|$$is equal to... COMEDK 2023 Morning Shift If$$A=\left[\begin{array}{cc}k+1 & 2 \\ 4 & k-1\end{array}\right]$$is a singular matrix, then possible values of$$\mathrm{k}$$are COMEDK 2023 Evening Shift$$ \text { If } A=\left(\begin{array}{ll} 1 & 2 \\ 0 & 1 \end{array}\right) \quad P=\left(\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta ...
COMEDK 2023 Evening Shift
$$A$$ and $$B$$ are invertible matrices of the same order such that $$\left|(A B)^{-1}\right|=8$$ if $$|A|=2$$ then $$|B|$$ is
COMEDK 2023 Evening Shift
If $$2 A+3 B=\left[\begin{array}{ccc}2 & -1 & 4 \\ 3 & 2 & 5\end{array}\right]$$ and $$A+2 B=\left[\begin{array}{lll}5 & 0 & 3 \\ 1 & 6 & 2\end{array}... COMEDK 2023 Evening Shift If$$\left[\begin{array}{ccc}2+x & 3 & 4 \\ 1 & -1 & 2 \\ x & 1 & -5\end{array}\right]$$is a singular matrix, then$$x$$is COMEDK 2023 Evening Shift Solution of$$x-y+z=4 ; x-2 y+2 z=9$$and$$2 x+y+3 z=1$$is COMEDK 2022 If for any 2$$\times$$2 square matrix A, A (adj A) =$$\left[ {\matrix{ 8 & 0 \cr 0 & 8 \cr } } \right]$$, then find the value of det (A... COMEDK 2022 If$$A = \left[ {\matrix{ a & 0 & 0 \cr 0 & a & 0 \cr 0 & 0 & a \cr } } \right]$$, then$$|A||adj\,A|$$is equal to COMEDK 2022 If$$A = \left[ {\matrix{ {2 - k} & 2 \cr 1 & {3 - k} \cr } } \right]$$is a singular matrix, then the value of$$5k - {k^2}$$is COMEDK 2021 If for any 2$$\times$$2 square matrix A, A (adj A) =$$\left[ {\matrix{ 8 & 0 \cr 0 & 8 \cr } } \right]$$, then the value of det (A).... COMEDK 2021 If matrix$$A = \left[ {\matrix{ 2 & { - 2} \cr { - 2} & 2 \cr } } \right]$$and$${A^2} = pA$$, then the value of$$p$$is COMEDK 2021 If$$A\,(adj\,A) = \left[ {\matrix{ { - 2} & 0 & 0 \cr 0 & { - 2} & 0 \cr 0 & 0 & { - 2} \cr } } \right]$$, then$$|adj\,A|$$equals... COMEDK 2020 If$$A = \left[ {\matrix{ 1 & { - 1} & 1 \cr 2 & 1 & { - 3} \cr 1 & 1 & 1 \cr } } \right],10B = \left[ {\matrix{ 4 & 2 & 2 \cr ...
COMEDK 2020
If $$A = \left[ {\matrix{ 0 & x & {16} \cr x & 5 & 7 \cr 0 & 9 & x \cr } } \right]$$ is singular, then the possible values of x are...
COMEDK 2020
If $$A = \left[ {\matrix{ 1 & { - 2} & 2 \cr 0 & 2 & { - 3} \cr 3 & { - 2} & 4 \cr } } \right]$$, then A . adj (A) is equal to
COMEDK 2020
The value of $$\left| {\matrix{ x & p & q \cr p & x & q \cr p & q & x \cr } } \right|$$ is
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