Sample Quiz for Feb 8, 2006

Linear Algebra

Which of the following are in Reduced Row Echelon Form? Circle the Pivot Positions in that matrix.

({{1, 0, 0, 2, 0, 0}, {0, 0, 1, 2, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}})

({{1, 0, 2, 0, 0, 0}, {0, 0, 1, 2, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}})

({{1, 0, 0, 2, 0, 0}, {0, 0, 1, 2, 0, 0}, {0, 0, 0, 0, 3, 0}, {0, 0, 0, 0, 0, 1}})

Use Gaussian Elimination to find the solutions to
    x_1 + x_4 = 1  x_1 + x_3 + 4x_4 = 2  3x_5 + 3x_6 = 12  x_6 = 3
Use only one elementary row operation at a time.

Solutions

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