Let x1, x2, x3 be linearly independent vectors in R4 and let A be a nonsingular 4

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Let x1, x2, x3 be linearly independent vectors in R4 and let A be a nonsingular 4 × 4 matrix. Prove that if
y1 = Ax1, y2 = Ax2, y3 = Ax3
then y1, y2, y3 are linearly independent.
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