Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question 1 а) Write down the 3 × 3 matrices A, B and C with entries ażj = i, bij = i/j and cij = i', respectively. Compute AB, BA and C². Find det(C). b) c) If det (M) = 2 and det(N) = 3, calculate: i det (NM-1N). 1 ii det (M®N°(M-!)“(N-1)³). d) Use the Gauss-Jordan algorithm to find the inverse of the following matrix 1 0 0 0 4 4 4 0 1 e) For the following system of equations write down the augmented matrix, find its reduced row echelon form and then use it to write down the solutions to the system x + 4y + 4z x + 8y + 8z 5x + 4y + 5z 1 1 -2. f) row echelon form and then use it to write down the solutions to the system For the following system of equations write down the augmented matrix, find its reduced 1 xi - x3 4x1 – 2x4 2x2 – 2x3 – X4 -2 1.
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Transcribed Image Text:Question 1 а) Write down the 3 × 3 matrices A, B and C with entries ażj = i, bij = i/j and cij = i', respectively. Compute AB, BA and C². Find det(C). b) c) If det (M) = 2 and det(N) = 3, calculate: i det (NM-1N). 1 ii det (M®N°(M-!)“(N-1)³). d) Use the Gauss-Jordan algorithm to find the inverse of the following matrix 1 0 0 0 4 4 4 0 1 e) For the following system of equations write down the augmented matrix, find its reduced row echelon form and then use it to write down the solutions to the system x + 4y + 4z x + 8y + 8z 5x + 4y + 5z 1 1 -2. f) row echelon form and then use it to write down the solutions to the system For the following system of equations write down the augmented matrix, find its reduced 1 xi - x3 4x1 – 2x4 2x2 – 2x3 – X4 -2 1.
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