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Ex 3.2, 15 - Chapter 3 Class 12 Matrices
Last updated at May 29, 2023 by Teachoo
Chapter 3 Class 12 Matrices
Concept wise
- Formation and order of matrix
- Types of matrices
- Equal matrices
- Addition/ subtraction of matrices
- Statement questions - Addition/Subtraction of matrices
- Multiplication of matrices
- Statement questions - Multiplication of matrices
-
Solving Equation
- Finding unknown - Element
- Finding unknown - Matrice
- Transpose of a matrix
- Symmetric and skew symmetric matrices
- Proof using property of transpose
- Inverse of matrix using elementary transformation
- Proof using mathematical induction
Transcript
Ex 3.2, 15 Find A2 5A + 6I if A = [ 8(2&0&[email protected]&1&[email protected]& 1&0)] Finding A2 A2 = AA = [ 8(2&0&[email protected]&1&[email protected]& 1&0)] [ 8(2&0&[email protected]&1&[email protected]& 1&0)] = [ 8(2(2)+0(2)+1(1)&2(0)+0(1)+1( 1)&2(1)+0(3)+1(0)@2(2)+1(2)+3(1)&2(0)+1(1)+3( 1)&2(1)+1(3)+3(0)@1(2)+ 1(2)+0(1)&1(0)+ 1(1)+0( 1)&1(1)+ 1(3)+0(0))] = [ 8(4+0+1&0+0 1&[email protected]+2+3&0+1 3&[email protected] 2+0&0 1+0&1 3+0)] = [ 8(5& 1&[email protected]& 2&[email protected]& 1& 2)] Now calculating A2 5A + 6I = [ 8(5& 1&[email protected]& 2&[email protected]& 1& 2)] 5 [ 8(2&0&[email protected]&1&[email protected]& 1&0)]+ 6 [ 8(1&0&[email protected]&1&[email protected]&0&1)] = [ 8(5& 1&[email protected]& 2&[email protected]& 1& 2)] [ 8(2 5&0 5&1 [email protected] 5&1 5&3 [email protected] 5& 1 5&0 5)] + [ 8(1 6&0 6&0 [email protected] 6&1 6&0 [email protected] 6&0 6&1 6)] = [ 8(5& 1&[email protected]& 2&[email protected]& 1& 2)] - [ 8(10&0&[email protected]&5&[email protected]& 5&0)] + [ 8(6&0&[email protected]&6&[email protected]&0&6)] = [ 8(5 10+6& 1 0+0&2 [email protected] 10+0& 2 5+6&5 [email protected] 5+0& 1+5+0& 2 0+6)] = [ 8(1& 1& 3@ 1& 1& 10@ 5&4&4)]
