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

Chapter 5, Problem 29

(choose chapter or problem)

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 \(\langle A, B\rangle=2 a_{11} b_{11}+a_{12} b_{12}+a_{21} b_{21}+2 a_{22} b_{22}\).

\(A=\left[\begin{array}{rr}2  -4 \\ -3  1\end{array}\right], \quad B=\left[\begin{array}{rr}-2  1 \\ 1  0\end{array}\right]\)

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 = [2  -4 \\ -3  1],     B = [-2  1 \\ 1  0]