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Problem 4. (10 points) If are arbitrary vectors in $\mathbb{R}^{2 \times 2}$, then the mapping $A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$ and $B = \begin{bmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{bmatrix}$ $(A, B) = a_{11}b_{11} + a_{12}b_{12} + a_{21}b_{21} + a_{22}b_{22}$ defines an inner product in $\mathbb{R}^{2 \times 2}$. Use this inner product to determine $(A, B)$, $||A||$, $||B||$, and the angle $\alpha_{A, B}$ between $A$ and $B$ for $(A, B) = \boxed{} ||A|| = \boxed{} ||B|| = \boxed{} $\alpha_{A, B} = \boxed{}$ (radians). Note: You can earn partial credit on this problem. A = $\begin{bmatrix} -5 & -4 \\ -1 & 4 \end{bmatrix}$ and B = $\begin{bmatrix} -3 & 3 \\ 2 & 1 \end{bmatrix}$

          Problem 4. (10 points)
If
are arbitrary vectors in $\mathbb{R}^{2 \times 2}$, then the mapping
$A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$ and $B = \begin{bmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{bmatrix}$
$(A, B) = a_{11}b_{11} + a_{12}b_{12} + a_{21}b_{21} + a_{22}b_{22}$
defines an inner product in $\mathbb{R}^{2 \times 2}$. Use this inner product to determine $(A, B)$, $||A||$, $||B||$, and the angle $\alpha_{A, B}$ between $A$ and $B$ for
$(A, B) = \boxed{}
||A|| = \boxed{}
||B|| = \boxed{}
$\alpha_{A, B} = \boxed{}$ (radians).
Note: You can earn partial credit on this problem.
A = $\begin{bmatrix} -5 & -4 \\ -1 & 4 \end{bmatrix}$ and B = $\begin{bmatrix} -3 & 3 \\ 2 & 1 \end{bmatrix}$

Problem 4. (10 points)
If
are arbitrary vectors in ℝ^2 × 2, then the mapping
A =
< b m a t r i x > and B =
< b m a t r i x >
(A, B) = a11b11 + a12b12 + a21b21 + a22b22
defines an inner product in ℝ^2 × 2. Use this inner product to determine (A, B), ||A||, ||B||, and the angle αA, B between A and B for
(A, B) =
||A|| =
||B|| =αA, B = (radians).
Note: You can earn partial credit on this problem.
A =
< b m a t r i x >
and B =
< b m a t r i x >

Added by Amparo H.

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