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    Matrices: Existence and Uniqueness of Solutions

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    1. Choose h and k such that the system has (a) no solution, (b) a unique solution and (c) many solutions.

    a) x_1 + hx_2 = 2
    4x_1 + 8x_2 = k

    b) x_1 + 3x_2 = 2
    3x_1 + hx_2 = k

    2. Explain existence and uniqueness and give examples using a matrix.

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    Solution Preview

    • For a system of equations to have a unique solution, the equations must not be linearly dependent. This implies that the rows of the matrix must be linearly independent.
    • For infinite number of solutions, ...

    Solution Summary

    This solution explains what makes a system have a unique solution, an infinite number of solutions, or now solutions.