Question: . (10pt) Let A E Matnxn be such that A = AT and Ax1 = 1X1, Ax2 = 12X2 and Al # 12. Prove that

. (10pt) Let A E Matnxn be such that A = AT and Ax1 = 1X1, Ax2 = 12X2 and Al # 12. Prove that X1 1 X2, i.e., xJ . X2 = 0. [Hint: consider . Ax, = XT . ATX2 = (Axl) . X2 and use that x1 and x2 are eigenvectors.]

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