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    Vectors

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    The set of vectors {[ 1 -1] , [ 1 -1] , [ 2 -1] }
    [ 2 0 ] [ -1 0] [ -1 0]

    from M_2(R) is:
    A. linearly dependent
    B. linearly independent
    C. orthogonal
    D. a spanning set for M_2(R)
    E. a basis for M_2(R)

    © BrainMass Inc. brainmass.com March 4, 2021, 5:52 pm ad1c9bdddf
    https://brainmass.com/math/vector-calculus/type-vector-matrix-15916

    Solution Preview

    I presume that each vector in this set is a 2*2 matrix. Then we have:

    {[ 1 -1] , [ 1 -1] , [ 2 -1] }
    [ 2 0 ] [ -1 0] [ -1 0]

    part a and b.

    Consider

    [1 -1]
    A1 :=
    [2 0]

    [1 -1]
    A2 :=
    [-1 0]

    [2 -1]
    A3 :=
    [-1 0]

    Then we define mA1+nA2+pA3=0 (zero matrix) and solve for m, n and p:

    ...

    Solution Summary

    This shows how to determine the type of vectors from a matrix.

    $2.19

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