Unformatted text preview: (v) ﬁnd the transpose of your matrix A in part (iii) above. 2. (2 marks each) Solve the following linear systems (if possible, if not state why the system is inconsistent), by row reduction : ( i ) 2 x 1 + 2 x 2x 33 x 5 = 0 3 x 1x 2 + 2 x 3x 4x 5 = 0 x 1 + x 2x 5 = 0 2 x 3 + 2 x 5 = 0 ( ii ) w + x2 y + z =3 3 w + 2 xy + 3 z =1w + 3 x + y4 z = 12 2 x + y4 z = 10 3. (3 marks) Solve the system in 2(ii) above by the method of matrix inversion . Can you use this method to solve the system in 2(i)? Justify your answer. 4. (2 marks each) Verify the following properties: (i) ( AB )1 = B1 A1 when A,B are distinct invertible 3 × 3 matrices of your choice. (ii) tr ( CD ) = tr ( DC ) when C is a 4 × 2 and D is a 2 × 4 matrix of your choice. (iii) ( A T )1 = ( A1 ) T for your matrix A above. (iv) A ( B + C ) = AB + AC for any 3 × 3 matrices of your choice....
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 Spring '09
 MihaiBeligan
 Linear Algebra, Algebra, matlab, Matrices, TA, Invertible matrix, 3W, lin alg

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