New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Matrices and Determinants question

2023 · 29 Jan · Shift 2 · Q44

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Matrices and Determinants
2023 · 29 Jan · Shift 2 · Q44

Matrices and Determinants question

2023 · 29 Jan · Shift 2 · Q44

JEE MainMathematicsMatrices and DeterminantsNumerical+4 / −1

Let A be a symmetric matrix such that

\mathrm{|A|=2}

and

\left[ {\begin{matrix} 2 & 1 \\ 3 & {{3 \over 2}} \\ \end{matrix} } \right]A = \left[ {\begin{matrix} 1 & 2 \\ \alpha & \beta \\ \end{matrix} } \right]

. If the sum of the diagonal elements of A is

s

, then

\frac{\beta s}{\alpha^2}

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Matrices and Determinants

Let the system of linear equations $x + y + k z = 22 x + 3 y - z = 13 x + 4 y + 2 z = k$ have infinitely many solutions. Then the system $(k + 1) x + (2 k - 1) y = 7 (2 k + 1) x + (k + 5) y = 10$ has :2023 · MCQ
For $α, β \in R$ , suppose the system of linear equations $x - y + z = 5 2 x + 2 y + α z = 8 3 x - y + 4 z = β$ has infinitely many solutions. Then $α$ and $β$ are…2023 · MCQ
For the system of linear equations $x + y + z = 6 α x + β y + 7 z = 3 x + 2 y + 3 z = 14$ which of the following is NOT true ?2023 · MCQ
Let $A = 1000412 0 - 1 - 3$ . Then the sum of the diagonal elements of the matrix $(A + I)^{11}$ is equal to :2023 · MCQ
The number of values of $α$ for which the system of equations : x + y + z = $-$ x + 2 $α$ y + 3z = $-$ 1 x + 3 $α$ y + 5z = 4 is inconsistent, is2022 · MCQ
Let the system of linear equations x + y + $α$ z = 2 3x + y + z = 4 x + 2z = 1 have a unique solution (x $^{*}$ , y $^{*}$ , z $α$ ). If ( $α$ , x $^{*}$ ), (y $α$ , $α$ ) and (x $-$ , $-$ y $^{*}$ ) are collinear points, then the…2022 · MCQ
Let $S = {(- 1 0 a b); a, b \in {1, 2, 3, ....100}}$ and let $T_{n} = {A \in S : A^{n (n + 1)} = I}$ . Then the number of elements in $n = 1 ⋂ 100 T_{n}$ …2022 · Numerical
The number of $θ \in (0, 4 π)$ for which the system of linear equations $3 (sin 3 θ) x - y + z = 2 3 (cos 2 θ) x + 4 y + 3 z = 3 6 x + 7 y + 7 z = 9$ has no solution, is :2022 · MCQ