Question

let be a matrix with linearly independent one of these statements must be true? you have only three attempts at this problem.

Answer 1

If a matrix has linearly independent rows, the rank of the matrix is equal to the number of rows, the determinant is non-zero, and the matrix is invertible.

Step-by-step explanation:

If a matrix has linearly independent rows, it means that no row can be written as a linear combination of the other rows. In other words, the rows are not redundant and provide unique information. Based on this, we can deduce that if a matrix has linearly independent rows:

1. The rank of the matrix is equal to the number of rows.
2. The determinant of the matrix is non-zero.
3. The matrix is invertible (i.e., it has an inverse).