New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Matrices and Determinants question

2021 · 24 Feb · Shift 1 · Q36

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

PYQ Library
JEE Main
Mathematics
Matrices and Determinants
2021 · 24 Feb · Shift 1 · Q36

Matrices and Determinants question

2021 · 24 Feb · Shift 1 · Q36

JEE MainMathematicsMatrices and DeterminantsNumerical+4 / −1

Let P =

\left[ {\begin{matrix} 3 & { - 1} & { - 2} \\ 2 & 0 & \alpha \\ 3 & { - 5} & 0 \\ \end{matrix} } \right]

, where

\alpha \in

R. Suppose Q = [ qij] is a matrix satisfying PQ = kl3 for some non-zero k

\in

R. If q23 =

- {k \over 8}

and |Q| =

{{{k^2}} \over 2}

, then a2 + k2 is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Matrices and Determinants

Let M be any 3 $\times$ 3 matrix with entries from the set {0, 1, 2}. The maximum number of such matrices, for which the sum of diagonal elements of MTM is seven, is .2021 · Numerical
Let A and B be 3 $\times$ 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations (A2B2 $-$ B2A2) X = O, where X is a 3 $\times$ 1 column matrix of unknown variables and O is a 3 $\times$ …2021 · MCQ
For the system of linear equations: $x - 2 y = 1, x - y + k z = - 2, k y + 4 z = 6, k \in R$ , consider the following statements : (A) The system has unique solution if $k e 2, k e - 2$ . (B) The system has unique solution if k = $-$ 2 (C) The…2021 · MCQ
If $A = [0 tan (\frac{θ}{2}) - tan (\frac{θ}{2}) 0]$ and $(I_{2} + A) (I_{2} - A)^{- 1} = [a b - b a]$ …2021 · Numerical
If the system of equations kx + y + 2z = 1 3x $-$ y $-$ 2z = 2 $-$ 2x $-$ 2y $-$ 4z = 3 has infinitely many solutions, then k is equal to .2021 · Numerical
Let A be a 3 $\times$ 3 matrix with det(A) = 4. Let Ri denote the ith row of A. If a matrix B is obtained by performing the operation R2 $\to$ 2R2 + 5R3 on 2A, then det(B) is equal to :2021 · MCQ
If for the matrix, $A = [1 α - α β]$ , $A A^{T} = I_{2}$ , then the value of $α^{4} + β^{4}$ is :2021 · MCQ
The following system of linear equations 2x + 3y + 2z = 9 3x + 2y + 2z = 9 x $-$ y + 4z = 82021 · MCQ