If A = [[(1/2)cos x, −sin x], [sin x, (1/2)cos x]] and A + A′ = I, then value of x ∈ [−π/2, π/2] is

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Properties of Matrix Addition, Symmetric Matrix | PadhAiPro

Question

MCQ (Single)Properties of Matrix AdditionSymmetric Matrix

Assertion (A) : For any symmetric matrix A, B′AB is a skew-symmetric matrix. Reason (R) : A square matrix P is skew-symmetric if P′ = – P.

If [2 0; 5 4] = P + Q, where P is a symmetric and Q is a skew symmetric matrix, then Q is equal to

MCQ (Single)Symmetric MatrixSkew-Symmetric Matrix

If A = [1 4 x; z 2 y; -3 -1 3] is a symmetric matrix, then the value of x + y + z is :

A and B are skew-symmetric matrices of same order. AB is symmetric, if :

For what value of x ∈ [0, π/2], is A + A′ = √3 I, where A = [cos x sin x; −sin x cos x] ?

Number of symmetric matrices of order 3 × 3 with each entry 1 or −1 is