Explore BrainMass

# Matrices: Existence and Uniqueness of Solutions

Not what you're looking for? Search our solutions OR ask your own Custom question.

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.

Â© BrainMass Inc. brainmass.com December 24, 2021, 5:10 pm ad1c9bdddf
https://brainmass.com/math/linear-algebra/matrices-existence-and-uniqueness-of-solutions-32345

#### Solution Preview

â€¢ 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.
â€¢ 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.

\$2.49