Matrices: Existence and Uniqueness of Solutions
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.
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