Question

2. (1 pt) If A = [a11 a12; a21 a22] and B = [b11 b12; b21 b22] are arbitrary vectors in M2(R), then the mapping <A, B> = a11b11 + a12b12 + a21b21 + a22b22 defines an inner product in M2(R). Use this inner product to determine <A, B>, ||A||, ||B||, and the angle ?aA,B between A and B for A = [5 -2; 4 -2] and B = [-5 -2; 1 1]. <A, B> = , ||A|| = , ||B|| = , aA,B = .

          2. (1 pt) If A = [a11 a12; a21 a22] and B = [b11 b12; b21 b22] are arbitrary vectors in M2(R), then the mapping <A, B> = a11b11 + a12b12 + a21b21 + a22b22 defines an inner product in M2(R). Use this inner product to determine <A, B>, ||A||, ||B||, and the angle ?aA,B between A and B for A = [5 -2; 4 -2] and B = [-5 -2; 1 1].
<A, B> = __________,
||A|| = __________,
||B|| = __________,
aA,B = __________.

2. (1 pt) If A = [a11 a12; a21 a22] and B = [b11 b12; b21 b22] are arbitrary vectors in M2(R), then the mapping <A, B> = a11b11 + a12b12 + a21b21 + a22b22 defines an inner product in M2(R). Use this inner product to determine <A, B>, ||A||, ||B||, and the angle ?aA,B between A and B for A = [5 -2; 4 -2] and B = [-5 -2; 1 1].
<A, B> = ,
||A|| = ,
||B|| = ,
aA,B = .

Added by Jason R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shaiju T

04/18/2022

Step 1

Step 1: Calculate A,B >: Given A = \begin{bmatrix} 5 & -2 \\ 4 & -2 \end{bmatrix} and B = \begin{bmatrix} -5 & -21 \\ 1 & 1 \end{bmatrix} A,B > = 5*(-5) + (-2)*(-21) + 4*1 + (-2)*1 A,B > = -25 + 42 + 4 - 2 A,B > = 19 Show more…

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2. (1 pt) If A = [a11 a12; a21 a22] and B = [b11 b12; b21 b22] are arbitrary vectors in M2(R), then the mapping <A, B> = a11b11 + a12b12 + a21b21 + a22b22 defines an inner product in M2(R). Use this inner product to determine <A, B>, ||A||, ||B||, and the angle aA,B between A and B for A = [5 -2; 4 -2] and B = [-5 -2; 1 1]. <A, B> = __________, ||A|| = __________, ||B|| = __________, aA,B = __________.