Review_mat343_1.pdf - Review#1 MAT343 Problem 1 Use Gaussian Elimination to solve the following system of linear equations x1 2x2 x3 x4 = 0 x1 2x2 3x3

Review_mat343_1.pdf - Review#1 MAT343 Problem 1 Use...

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Review # 1, MAT343 Problem 1: Use Gaussian Elimination to solve the following system of linear equations: x 1 + 2 x 2 - x 3 + x 4 = 0 - x 1 - 2 x 2 + 3 x 3 + 5 x 4 = 0 - x 1 - 2 x 2 - x 3 - 7 x 4 = 0 Problem 2: Consider the matrix: A = 1 2 3 4 1 4 5 8 1 1 2 3 1 3 5 8 a) Use the elimination method to evaluate det( A ). b) Use the value of det( A ) to evaluate the determinant the matrix B , where B = 3 6 9 12 1 3 5 8 1 4 5 8 1 1 2 3 Problem 3: Let A = 3 6 - 9 2 5 - 3 - 4 1 10 a) Use Row operation III to find an upper triangular matrix U and elementary matrices E 1 , E 2 and E 3 such that E 3 E 2 E 1 A = U . b) Determine the inverses of E 1 , E 2 and E 3 ; and find the matrix L such that A = LU . 1
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Problem 4: Consider the matrix A = 1 1 1 1 2 t 1 4 t 2 a) Use the elimination method to evaluate det( A ) in terms of t . b) Find all possible choices of t that would make the matrix A singular.
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