Explore BrainMass

Explore BrainMass

    Matrices: Existence and Uniqueness of Solutions

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com March 4, 2021, 6:09 pm ad1c9bdddf

    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.