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

**Chapter 3, Problem 18**

(choose chapter or problem)

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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