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    The reduced row-echelon forms of the augmented matrices of three systems are given below. How many solutions does each system have?

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    The reduced row-echelon forms of the augmented matrices of three systems are given in the attachment. How many solutions does each system have?

    1. The reduced row-echelon forms of the augmented matrices of three systems are given below. How many solutions does each system have?

    a. │1 0 2 0│
    │0 1 3 0│
    │0 0 0 1│

    b. │1 0 5│
    │0 1 6│

    c. │0 1 0 2│
    │0 0 1 3│

    4. Find the rank of the matrix.

    │ 1 4 7 │
    │ 2 5 8 │
    │ 3 6 9 │

    36. Find a 3x3 matrix A such that

    ┌ ┐ ┌ ┐
    │ 1 │ │ 1 │
    A = │ 0 │ = │ 2 │,
    │ 0 │ │ 3 │
    └ ┘ └ ┘

    ┌ ┐ ┌ ┐
    A = │ 0 │= │ 4 │ , and
    │ 1 │ │ 5 │
    │ 0 │ │ 6 │
    └ ┘ └ ┘

    ┌ ┐ ┌ ┐
    │ 0 │ │ 7 │
    A = │ 0 │= │ 8 │
    │ 1 │ │ 9 │
    └ ┘ └ ┘

    58. For which values of the constants b and c is the vector

    ┌ ┐
    │3│ a linear combination of
    │b│
    │c│
    └ ┘
    ┌ ┐
    │1│
    │3│,
    │2│
    └ ┘
    ┌ ┐
    │2│
    │6│, and
    │4│
    └ ┘
    ┌ ┐
    │-1│
    │-3│ ?
    │-2│
    └ ┘

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    https://brainmass.com/math/linear-algebra/reduced-row-echelon-forms-augmented-matrices-31883

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