Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

NTA Abhyas JEE Main2020MathematicsMatricesPractice

If A is a skew symmetric matrix of order 3 , B is a 3 × 1 column matrix and C = B T A B , then which of the following is false?

Options

AC is singular
BC is non singular
CC is a symmetric matrix
DC is a skew symmetric matrix

Correct answer

B. C is non singular

Step-by-step solution

Given, C = B T A B C T = B T A B T ⇒ C T = B T A T B T T ⇒ C T = - B T A B = - C ⇒ C is skew symmetric ∵ order of C is 1 × 1 ⇒ C = 0 ⇒ C is singular and symmetric also.

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? 2026 Consider 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 2026 For 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 2026 Let 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 2026 Let 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: 2026 Let 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 : 2026 Let 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 2026 Let 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 NTA Abhyas JEE Main PYQs