Ex 4.4

Chapter 4 Class 12 Determinants
Serial order wise

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### Transcript

Ex 4.4, 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 Nonsingular: Where |𝐴|≠ 0 Ex 4.4, 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)| (|𝐴𝐵|=|𝐴||𝐵|) 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| |adj (A)| = |A|2 Thus, B is the correct answer Since |A| is Constant Using Property |kA| = kn |A| where n is order of A

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.