![Ex 4.1, 3 - Show that |2A| = 4|A|, if A = [1 2 4 2] - Ex 4.1](https://d1avenlh0i1xmr.cloudfront.net/d597ceeb-2b0f-491e-8d73-8dc7b11e0c2a/slide4.jpg)
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Ex 4.1, 3 - Chapter 4 Class 12 Determinants (Term 1)
Last updated at March 22, 2023 by Teachoo
Chapter 4 Class 12 Determinants
Serial order wise
Transcript
Ex 4.1, 3 If A = [■8(1&[email protected]&2)] , then show that |2A| = 4|A| We need to prove |2A| = 4|A| Taking L.H.S |2A| First calculating 2 A 2A = 2 [■8(1&[email protected]&2)] = [■8( 2 × 1&2 × [email protected] 2 × 4&2 × 2)] = [■8(2&[email protected]&4)] So, |2A| = |■8(2&[email protected]&4)| = 2(4) – 8 (4) = 8 – 32 = –24 Taking R.H.S 4|A| As A = [■8(1&[email protected]&2)] So |A| = |■8(1&[email protected]&2)| = 1 (2) – 4 (2) = 2 – 8 = –6 Hence, 4|A| = 4 (−6) = −24 = L.H.S ∴ L.H.S = R.H.S Hence proved
