Consider the following augmented matrix Determine the values of k for which the system has (i)...
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Consider the following augmented matrix Determine the values of k for which the system has (i) no solution, (ii) exactly one solution, (iii) infinitely many solutions. Question 12: 4 Marks Consider the matrices 1 3 -4 Question 11: 5 Marks Assume that A and B are matrix of the same size. Prove or Disprove that (A + B)2 is a symmetric, skew- symmetric or neither. (12.2) E₁B A, (12.3) E₂A = C, (12.4) E3C = A. -1 -1 2 A = 2 5 k²-8 -2 7 1 8 1 5 3 4 1 Find elementary matrices Eo, E₁, E2 and E3 such that (12.1) EA B, B = 8 1 5 3 4 1 1 1 -2 k +2 -2 7 9 C = -2 7 1 3 4 1 27 3 (1) 5 (1) (1) (1) Consider the following augmented matrix Determine the values of k for which the system has (i) no solution, (ii) exactly one solution, (iii) infinitely many solutions. Question 12: 4 Marks Consider the matrices 1 3 -4 Question 11: 5 Marks Assume that A and B are matrix of the same size. Prove or Disprove that (A + B)2 is a symmetric, skew- symmetric or neither. (12.2) E₁B A, (12.3) E₂A = C, (12.4) E3C = A. -1 -1 2 A = 2 5 k²-8 -2 7 1 8 1 5 3 4 1 Find elementary matrices Eo, E₁, E2 and E3 such that (12.1) EA B, B = 8 1 5 3 4 1 1 1 -2 k +2 -2 7 9 C = -2 7 1 3 4 1 27 3 (1) 5 (1) (1) (1)
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