Question

Check if two vectors are linearly independent calculator.
a) True
b) False

Answer 1

To check if two vectors are linearly independent, we can use the determinant method. Arrange the components of the vectors in a matrix and calculate the determinant. If the determinant is zero, the vectors are linearly dependent.

Step-by-step explanation:

To check if two vectors are linearly independent, we can use the determinant method. Here are the steps:

1. Arrange the components of the vectors as rows in a matrix.
2. Calculate the determinant of the matrix.
3. If the determinant is non-zero, the vectors are linearly independent. If the determinant is zero, the vectors are linearly dependent.

For example, suppose we have two vectors A = (2, 3) and B = (4, 6). We can arrange them in a matrix form as:

[ 2 3 ]

[ 4 6 ]

Calculating the determinant of this matrix gives us:

Determinant = (2 * 6) - (3 * 4) = 12 - 12 = 0

Since the determinant is zero, the vectors A and B are linearly dependent.