Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsMatrices

If a singular matrix A= [a_ i j ]_ 2 2 always commute with B= [ array ll 1 & 1 2 & 1 array ] such that a₁₁ a₁₂ = k , then k is equal to___

Correct answer

2

Step-by-step solution

[ array ll a₁₁ & a₁₂ a₂₁ & a₂₂ array ] [ array ll 1 & 1 2 & 1 array ]= [ array ll 1 & 1 2 & 1 array ] [ array ll a₁₁ & a₁₂ a₂₁ & a₂₂ array ] a₁₁+2 a₁₂=a₁₁+a₂₁ (i) a₁₁+a₁₂=2 a₁₂+a₂₂ (ii) aligned & a₂₁+2 a₂₂=2 a₁₁+a₂₁ & a₂₁+a₂₂=2 a₁₂+a₂₂ aligned aligned & From (ii), a₁₁=a₂₂ & a₂₁=2 a₁₂ aligned aligned & a₁₁ a₂₂=a₂₁ a₂₁ (a₁₁ )^2=2 (a₁₂ )^2 & a₁₁= 2 a₁₂ aligned

Practice Matrices on Quantrex Academy →

More from Matrices

Which one of the following matrices can be obtained by performing elementary row transformations on the 3 3 identity matrix? 2026Consider the matrix M = bmatrix 2 & -1 1 & 0 bmatrix . Let p, q, r, s, a, b, c and d be integers such that M²⁶ = bmatrix p & q r & s bmatrix and _ k=1 ²⁶ M^k = bmatrix a & b c & d 2026For real numbers , , , and , consider the matrix M = bmatrix & 1 2 & - 1 2 1 3 & & 1 3 & & bmatrix . Suppose that MM^T = I , where M^T is the transpose of the matrix M , and I is t 2026Let R denote the set of all real numbers and let i = -1 . Consider the matrices S = bmatrix 0 & -1 1 & 0 bmatrix and T = bmatrix 1 & 1 0 & 1 bmatrix . Let a, b, c, d be real number 2026Let A = bmatrix & 1 & 2 2 & 3 & 0 0 & 4 & 5 bmatrix and B = bmatrix 1 & 0 & 0 0 & -5 & 0 0 & 4 & -2 bmatrix + adj (A) . If (B)=66 , then ( adj (A)) equals: 2026Let A = bmatrix 1 & 0 & 0 3 & 1 & 0 9 & 3 & 1 bmatrix and B = [b_ ij ] , 1 i, j 3 . If B = A⁹⁹ - I , then the value of b₃₁ - b₂₁ b₃₂ is : 2026Let A = bmatrix -1 & 1 & -1 1 & 0 & 1 0 & 0 & 1 bmatrix satisfy A^2 + (adj(adj(A))) + (adj(A)(adj(adj(A)))) = bmatrix 2 & -2 & 2 -2 & 0 & -1 0 & 0 & -1 bmatrix for some , R . Then 2026Let M be a 3 3 matrix such that M pmatrix 1 0 0 pmatrix = pmatrix 1 2 3 pmatrix , M pmatrix 0 1 0 pmatrix = pmatrix 0 1 2 pmatrix and M pmatrix 0 0 1 pmatrix = pmatrix -1 1 1 pmatr 2026 Full Matrices list All Most Important Selected Qs for JEE Advanced PYQs