Example 17 - Chapter 3 Class 12 Matrices (Term 1)
Last updated at Jan. 17, 2020 by Teachoo
Examples
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Example 4
Example 5 Important
Example 6
Example 7
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Example 10
Example 11 Important
Example 12
Example 13 Important
Example 14
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Example 16 Important
Example 17 You are here
Example 18 Important
Example 19
Example 20 Important
Example 21
Example 22 Important
Example 23
Example 24 Important
Example 25 Important
Example 26 Important
Example 27 Important
Example 28
Chapter 3 Class 12 Matrices
Serial order wise
Transcript
Example 17 If A = [■8(0&6&[email protected]−6&0&[email protected]&−8&0)], B = [■8(0&1&[email protected]&0&[email protected]&2&0)] , C = [█([email protected]−[email protected])] Calculate AC, BC and (A + B)C. Also, verify that (A + B)C = AC + BC Calculating AC AC = [■8(0&6&[email protected]−6&0&[email protected]&8&0)]_(3 × 3) [█([email protected]−[email protected])]_(3 × 1) = [█(0(2)+6(−2)+7(3)@−6(2)+0(−2)+8(3)@7(2)+8(−2)+0(3))]_(3 × 1) = [█(0−[email protected]−[email protected]+16+0)] = [█([email protected]@30)] Calculating BC BC = [■8(0&1&[email protected]&0&[email protected]&2&0)]_(3 × 3) [█([email protected]−[email protected])]_(3 × 1) = [█(0(2)+1(−2)+1(3)@1(2)+0(−2)+2(3)@1(2)+2(−2)+0(3))]_(3 × 1) = [█(0−[email protected][email protected]−4+0)] = [█([email protected]@−2)] Calculating AC + BC AC + BC =[█([email protected]@30)] + [█([email protected]@−2)] = [█([email protected][email protected]−2)] = [█([email protected]@28)] Calculating (A + B) C First calculating A + B A + B = [■8(0&6&[email protected]−6&0&[email protected]&−8&0)] +[■8(0&1&[email protected]&0&[email protected]&2&0)] = [■8(0+0&6+1&[email protected]−6+1&0+0&[email protected]+1&−8+2&0+0)] = [■8(0&7&[email protected]−5&0&[email protected]&−6&0)] Now, Calculating (A + B) C (A + B) C = [■8(0&7&[email protected]−5&0&[email protected]&−6&0)]_(3 × 3) [█([email protected]−[email protected])]_(3 × 1) = [█(0(2)+7(−2)+8(3)@−5(2)+0(−2)+10(3)@8(2)+(−6)(−2)+0(3))]_(3 × 1) = [█(0−[email protected]−[email protected]+12+0 )] = [█([email protected]@28)] = AC + BC ∴ L.H.S. = R.H.S. Hence proved
