matrices help?

For what value of c does the linear system with augmented matrix

1 0 0 1

0 1 c 2

0 0 1 3

have the unique solution x1=1, x2=-7,x3=3?

2 Answers

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  • Alan
    Lv 7
    4 weeks ago
    Best Answer

    1 0 0 1

    0 1 c 2

    0 0 1 3

    Use echelon row reduction to find the solution

    subtract (c) times row 3 from row 2

    1 0 0 1

    0 1 0 (2-3c)

    0 0 1 3

    so you now know

    x_1 =1

    x_2 = (2-3c )

    x_3 = 3

    so two items contain no c value and already correct.

    x_2 = 2-3c

    x_2= -7

    2 -3c = -7

    -3c = -9

    c = -9/-3 = 3

    answer

    c = 3

  • JOHN
    Lv 7
    4 weeks ago

    Answer

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