+1 vote
in Finite Element Method by (110k points)
In matrix algebra, a matrix K equals \(\begin{pmatrix} 1&0&0 \\ 0&1&0 \\ 0&0&3 \end{pmatrix}\). What is the value of a, if K^7 = \(\begin{pmatrix} c&0&0\\ 0&b&0 \\ 0&0&a \end{pmatrix}\)?

(a) 2187

(b) 729

(c) 6561

(d) 5^7

I have been asked this question in an online quiz.

The above asked question is from Eigen Value and Time Dependent Problems in chapter Single Variable Problems of Finite Element Method

1 Answer

+2 votes
by (185k points)
selected by
Best answer
Correct option is (a) 2187

Easiest explanation: Since K is a diagonal matrix, its higher powers are obtained by raising its diagonal elements to the same power. If K=\(\begin{pmatrix} 1&0&0 \\ 0&1&0 \\ 0&0&3 \end{pmatrix}\) then K^7=\(\begin{pmatrix} 1^7&0&0 \\ 0&1^7&0 \\ 0&0&3^7\end{pmatrix}\). Equating the corresponding elements of \(\begin{pmatrix} c&0&0\\ 0&b&0 \\ 0&0&a \end{pmatrix}\) and \(\begin{pmatrix} 1^7&0&0 \\ 0&1^7&0 \\ 0&0&3^7\end{pmatrix}\) we get



Related questions

We welcome you to Carrieradda QnA with open heart. Our small community of enthusiastic learners are very helpful and supportive. Here on this platform you can ask questions and receive answers from other members of the community. We also monitor posted questions and answers periodically to maintain the quality and integrity of the platform. Hope you will join our beautiful community