For any 3 × 3 matrix M , let | M | denote the determinant of M . Let E = 1 2 3 2 3 4 8 13 18 , P = 1 0 0 0 0 1 0 1 0 & F = 1 3 2 8 18 13 2 4 3 If Q is a nonsingular matrix of order 3 × 3 , then which of the following statement

Question

For any 3 &#215; 3 matrix M , let | M | denote the determinant of M . Let E = 1 2 3 2 3 4 8 13 18 , P = 1 0 0 0 0 1 0 1 0 &#38; F = 1 3 2 8 18 13 2 4 3 If Q is a nonsingular matrix of order 3 &#215; 3 , then which of the following statements is (are) TRUE ?

Quantrex Academy · Accepted Answer

Correct answer: A. F = P E P and P 2 = 1 0 0 0 1 0 0 0 1

(1) P 2 = 1 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 = 1 0 0 0 1 0 0 0 1 = I PEP = 1 0 0 0 0 1 0 1 0 1 2 3 2 3 4 8 13 18 1 0 0 0 0 1 0 1 0 = 1 2 3 8 13 18 2 3 4 1 0 0 0 0 1 0 1 0 = 1 3 2 8 18 13 2 4 3 = F (2) Here, F = P E P &#8658; P F = P 2 E P &#8658; P F = E P , E = 0 , &#160; F = 0 E Q + P F Q - 1 = E Q + E P Q - 1 = &#8739; E Q + P Q - 1 | = | E | | Q + P Q - 1 &#8739; = 0 | E Q | + P F Q - 1 = 0 + 0 = 0 (3) Since, | E | = 0 &#8658; | E F | = 0 Thus, E F 3 &#62; E F 2 is not possible (4) P = 1 0 0 0 0 1 0 1 0 &#8658

For any 3 × 3 matrix M , let | M | denote the determinant of M . Let E = 1 2 3 2 3 4 8 13 18 , P = 1 0 0 0 0 1 0 1 0 & F = 1 3 2 8 18 13 2 4 3 If Q is a nonsingular matrix of order 3 × 3 , then which of the following statements is (are) TRUE ?

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Correct answer

Step-by-step solution

More from Matrices

For any 3 &#215; 3 matrix M , let | M | denote the determinant of M . Let E = 1 2 3 2 3 4 8 13 18 , P = 1 0 0 0 0 1 0 1 0 &#38; F = 1 3 2 8 18 13 2 4 3 If Q is a nonsingular matrix of order 3 &#215; 3 , then which of the following statements is (are) TRUE ?

Options

Correct answer

Step-by-step solution

More from Matrices

For any 3 × 3 matrix M , let | M | denote the determinant of M . Let E = 1 2 3 2 3 4 8 13 18 , P = 1 0 0 0 0 1 0 1 0 & F = 1 3 2 8 18 13 2 4 3 If Q is a nonsingular matrix of order 3 × 3 , then which of the following statements is (are) TRUE ?