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## Solution for problem 18 Chapter 3.3

# Let A be a 3 3 matrix and let x1, x2, and x3 be vectors in R3. Show that if the vectors

Linear Algebra with Applications | 8th Edition

Problem 18

Let A be a 3 3 matrix and let x1, x2, and x3 be vectors in R3. Show that if the vectors y1 = Ax1, y2 = Ax2, y3 = Ax3 are linearly independent, then the matrix A must be nonsingular and the vectors x1, x2, and x3 must be linearly independent. 1

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###### Chapter 3.3, Problem 18 is Solved

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Let A be a 3 3 matrix and let x1, x2, and x3 be vectors in R3. Show that if the vectors