Ex 4.5, 17

Transcript

Ex 4.5, 17 (Method 1) Let A be a nonsingular square matrix of order 3 × 3. Then adj A﷯ is equal to A. A﷯ B. A﷯2 C. A﷯3 D. 3 A﷯ We know that 𝑎𝑑𝑗 𝐴﷯ = 𝐴﷯﷮𝑛 − 1﷯ where n is the order of Matrix A Here, n = 3 𝑎𝑑𝑗 𝐴﷯ = 𝐴﷯﷮3 − 1﷯ = 𝐴﷯﷮2﷯ Hence, B is the correct answer Ex 4.5, 17 (Method 2) Let A be a nonsingular square matrix of order 3 × 3. Then adj A﷯ is equal to A. A﷯ B. A﷯2 C. A﷯3 D. 3 A﷯ We know that A (adj A) = |A|I Taking determinants both sides |A (ad jA)| = ||A|I| Solving |A (adj (A))| |A (adj (A))| = |A| |adj (A)| Solving ||A|I| ||A|I| = |A|3|I| = |A|3 Now, |A (ad jA)| = ||A|I| Putting values |A| |adj (A)| = |A|3 |adj (A)| = A﷯3﷮ A﷯﷯ = |A|2 Thus, B is the correct answer