Question

Linearly independent columns calculator.

A) Linear independence cannot be determined by a calculator.
B) Multiply the columns and check for a nonzero result.
C) Use row reduction to check for linear independence.
D) Sum the columns and check for a zero result.

Answer 1

To determine if the columns of a matrix are linearly independent, you can use row reduction.

Step-by-step explanation:

To determine if the columns of a matrix are linearly independent, you can use row reduction. Here are the steps:

Take the transpose of the matrix. This switches the columns to rows.

Perform row reduction on the transposed matrix.

If you find a row of zeros, it means that the corresponding column in the original matrix is linearly dependent.

If there are no rows of zeros, it means that all columns are linearly independent.

Therefore, the correct answer is C) Use row reduction to check for linear independence.