01. For each of the following systems of equations, do the following: 1. Write down the corresponding augmented matrix. 2. Use Gaussian elimination to transform the augmented matrix into row-echelon form. 3. Solve the system of equations. (a) x1 - 2x2 + 3x3 = 11 2x1 - x2 + 3x3 = 10 4x1 + x2 - x3 = 4 (b) 2x1 - 2x2 + 4x3 = -3 3x1 - 3x2 + 6x3 = -4 5x2 + 2x3 = 9 (c) x1 + 2x2 + 4x3 = 10 -3x1 + 3x2 + 15x3 = 15 -2x1 - x2 + x3 = -5 (d) x1 - 4x2 - 5x3 = 11 2x1 - x2 - x3 = 2 3x1 + 9x2 + 12x3 = 30
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For System 1: ``` [ 1 -2 3 | 1] [ 0 3 -3 | 2] [ 0 0 2 | -2] ``` For System 2: ``` [ 1 -1 -2 | 5] [ 0 1 2 | -5] [ 0 0 1 | 1] ``` For System 3: ``` [ 1 2 4 | 10] [ 0 1 3 | 5] [ 0 0 1 | -1] ``` Show more…
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Solve the system of equations by using an augmented matrix. (You can use an online row reduction calculator as illustrated in the lectures) 3 x1 + 5 x2 - x3 = -17 x1 + x2 + x3 = -3 2 x1 + 3 x2 + 11x3 = 1
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Use elementary row operations to transform the augmented coefficient matrix to echelon form. Then solve the system by back substitution. x1 - 4x2 + 5x3 = 18 2x1 + x2 + x3 = 0 -4x1 + 3x2 - 2x3 = -15 An echelon form for the augmented coefficient matrix is
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