JEE MAIN Matrices Previous Year Questions (PYQs) – Page 3 of 15
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Let $A = [a_{ij}]_{2\times 2}$, where $a_{ij}\ne 0$ for all $i,j$ and $A^{2}=I$.
Let $a$ be the sum of all diagonal elements of $A$ and $b=\lvert A\rvert$ (i.e., $b=\det A$).
Then $3a^{2}+4b^{2}$ is equal to:
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Solution
If the system of linear equations
$2x+2y+3z=a$
$3x-y+5z=b$
$x-3y+2z=c$
where $a,b,c$ are non-zero real numbers, has more than one solution, then :
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Solution
The number of values of $k$, for which the system of equations : $\matrix{
{\left( {k + 1} \right)x + 8y = 4k} \cr
{kx + \left( {k + 3} \right)y = 3k - 1} \cr
} $
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Solution
Let $P$ be a square matrix such that $P^{2}=I-P$.
For $\alpha,\beta,\gamma,\delta\in\mathbb{N}$, if
$P^{\alpha}+P^{\beta}=\gamma I-29P$ and $P^{\alpha}-P^{\beta}=\delta I-13P$,
then $\alpha+\beta+\gamma-\delta$ is equal to:
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Solution
If the system of linear equations
$x + ay + z = 3$
$x + 2y + 2z = 6$
$x + 5y + 3z = b$
has no solution, then :
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Solution
Consider the matrix
$f(x)=\begin{bmatrix}
\cos x & -\sin x & 0\\
\sin x & \cos x & 0\\
0 & 0 & 1
\end{bmatrix}$.
Given below are two statements:
Statement I : $f(-x)$ is the inverse of the matrix $f(x)$.
Statement II : $f(x)f(y)=f(x+y)$.
In the light of the above statements, choose the correct answer:
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Solution
If $A = \left( {\matrix{ {{1 \over {\sqrt 5 }}} & {{2 \over {\sqrt 5 }}} \cr {{{ - 2} \over {\sqrt 5 }}} & {{1 \over {\sqrt 5 }}} \cr } } \right)$, $B = \left( {\matrix{ 1 & 0 \cr i & 1 \cr } } \right)$, $i = \sqrt { - 1} $, and Q = ATBA, then the inverse of the matrix A Q2021 AT is equal to :
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Solution
For the system of equations
\[
\begin{cases}
x+y+z=6,\\
x+2y+\alpha z=10,\\
x+3y+5z=\beta,
\end{cases}
\]
which one of the following is **NOT** true?
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Solution
Suppose $A$ is any $3\times 3$ non-singular matrix and $(A-3I)(A-5I)=0$ where $I=I_{3}$ and $O=O_{3}$. If $\alpha A+\beta A^{-1}=4I$, then $\alpha+\beta$ is equal to :
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Solution
Let $A = \left( {\matrix{ 1 & 0 & 0 \cr 0 & 1 & 1 \cr 1 & 0 & 0 \cr } } \right)$. Then A2025 $-$ A2020 is equal to :
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Solution
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