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    Matrices: Vectors and Planes

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    1) Let v_1 = 1 v_2 = -3 and y = h.
    [ 0 ] [ 8 ] [-5]
    [-2 ] [ 8 ] [-3]
    For what value of h is y in the plane generated by v_1 and v_2?

    2) Compute the product why (a) the definitions and (b) the raw vector rule.

    8 3 -4 * 1
    5 1 2 * 1
    * 1

    3) Write the given linear system first as a vector equation and then as a matrix.

    8x_1 - x_2 = 4
    5x_1 + 4x_2 = 1
    x_1 - 3x_2 = 2

    4) Given A and B, write the augmented matrix for the linear system that corresponds to the matrix eg. Ax = b. Then solve the system and write the solution as a vector

    A = 1 2 1
    -3 -1 2
    0 5 3

    b = 0
    1
    -1

    © BrainMass Inc. brainmass.com March 4, 2021, 6:09 pm ad1c9bdddf
    https://brainmass.com/math/linear-algebra/matrices-vectors-and-planes-32348

    Solution Preview

    1. From the condition, we know that y = av1 + bv2 for some real numbers a, b. So we get a system of equations.

    (see attached)

    From the last two equations, we can ...

    Solution Summary

    Matrix problems involving vectors and planes, products and Ax = b are investigated in this solution. The solution is provided in an attached Word document.

    $2.49

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