Solved: Finding Inner Product, Length, and Distance In Exercises 2932, find (a) A, B

Chapter 5, Problem 32

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Finding Inner Product, Length, and Distance In Exercises 29 - 32, find (a) \(\langle A, B \rangle\), (b) \(||A\||\), (c) \(||B||\), and (d) \(d(A, B)\) for the matrices in \(M_{2,2}\) using the inner product \(\langle A, B\rangle=2 a_{11} b_{11}+a_{12} b_{12}+a_{21} b_{21}+2 a_{22} b_{22}\)

\(A=\left[\begin{array}{rr}1  0 \\ 0  -1\end{array}\right], \quad B=\left[\begin{array}{rr}1  1 \\ 0  -1\end{array}\right]\)

Text Transcription:

langle A, B rangle

||A\||

||B||

d(A, B)

M_{2,2}

langle A, Brangle = 2 a_11 b_11 + a_12 b_12 + a_21 b_21 + 2 a_22 b_22

A = [1  0 \\ 0  -1],     B = [1  1 \\ 0  -1]