# 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 Summary

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

##### 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, ...

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