Question

Explain how a calculator can be used to check whether a set of vectors is linearly independent.

Answer 1

A calculator can be used to check whether a set of vectors is linearly independent by performing calculations and analyzing the results using row reduction. Enter the vectors into the calculator in matrix form, use the row reduction function to find the row-reduced echelon form, and determine if there is a row of all zeros.

Step-by-step explanation:

A calculator can be used to check whether a set of vectors is linearly independent by performing calculations and analyzing the results. Here are the steps:

1. Enter the vectors into the calculator in matrix form. Each vector should be a row in the matrix.
2. Use the calculator's row reduction function (e.g., Gaussian elimination or reduced row echelon form) to find the row-reduced echelon form of the matrix.
3. If the row-reduced echelon form has a row of all zeros, then the vectors are linearly dependent. Otherwise, they are linearly independent.

For example, let's say we have the vectors v1 = [1, 2, 3] and v2 = [4, 5, 6]. We can enter them into the calculator as a matrix:

[1, 2, 3]

[4, 5, 6]

Then, we can use the calculator's row reduction function to get the row-reduced echelon form:

[1, 0, -1]

[0, 1, 2]

This means that the vectors v1 and v2 are linearly independent.