Question

What is the magnitude of the transformation of the matrices:

matrix{[6 0],[0 6]}
Option 1: 36
Option 2: 12
Option 3: 6
Option 4: 0

Answer 1

The magnitude of the transformation of the given matrix is the determinant, which is computed by multiplying the entries of the main diagonal (6 * 6), resulting in a magnitude of 36.

Step-by-step explanation:

You've asked about the magnitude of the transformation of the matrices given by matrix{[6 0],[0 6]}. In matrix terminology, this transformation is a scaling transformation, where the matrix can scale vectors in 2-dimensional space. The magnitude of this transformation can be understood as the determinant of the matrix, which is calculated by multiplying the entries on the main diagonal and subtracting the product of the off-diagonal entries:

Determinant = 6 * 6 - 0 * 0

The determinant or magnitude here is 36; hence, the correct answer is Option 1: 36.