MHT CET202617 April 2026Morning ShiftMathematicsMatricesActual
If the matrix A = bmatrix 4 & 1 3 & 2 bmatrix is expressed as the sum of a symmetric matrix B and a skew symmetric matrix C then which of the following relations is correct?
Options
- A|A| = |B| |C|
- B|A| = |B| + |C|
- C|C| = 0
- D|A| = |B|
Correct answer
B. |A| = |B| + |C|
Step-by-step solution
Given A = bmatrix 4 & 1 3 & 2 bmatrix The transpose of matrix A is A^T = bmatrix 4 & 3 1 & 2 bmatrix Any square matrix can be expressed as the sum of a symmetric matrix B and a skew-symmetric matrix C , where B = 1 2 (A + A^T) and C = 1 2 (A - A^T) B = 1 2 ( bmatrix 4 & 1 3 & 2 bmatrix + bmatrix 4 & 3 1 & 2 bmatrix ) = bmatrix 4 & 2 2 & 2 bmatrix C = 1 2 ( bmatrix 4 & 1 3 & 2 bmatrix - bmatrix 4 & 3 1 & 2 bmatrix ) = bmatrix 0 & -1 1 & 0 bmatrix Calculating the determinants of A , B , and C : |A| = (4)(2) - (1)(3)