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.If A=[[4,-1],[-1,k]]such that A^(2)-6A+...

.If `A=[[4,-1],[-1,k]]`such that `A^(2)-6A+7I=0,` then k=.

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If a=(1)/(7)(2hat(i)+3hat(j)+6hat(k)): b=(1)/(7)(6hat(i)+2hat(j)-3hat(k)): c=c_1hat(i)+c_2hat(j)+c_2hat(k) and matrix A=[[(2)/(7), (3)/(7), (6)/(7)], [(6)/(7), (2)/(7), -(3)/(7)], [c_1, c_2, c_3]] and AT^(T)=I , then c