Question

If A and B are arbitrary real m × n matrices, then the mapping ?A, B? = trace(A^T B) defines an inner product in ?^{m×n}. Use this inner product to find ?A, B?, the norms ||A|| and ||B||, and the angle (in radians) ?_{A,B} between A and B for A = egin{bmatrix} 2 & -3 \ -1 & 1 \ -2 & -2 end{bmatrix} and B = egin{bmatrix} -3 & -3 \ 3 & -1 \ 2 & -1 end{bmatrix}. ?A, B? = ||A|| = ||B|| = ?_{A,B} =

          If A and B are arbitrary real m × n matrices, then the mapping

?A, B? = trace(A^T B)

defines an inner product in ?^{m×n}. Use this inner product to find ?A, B?, the norms ||A|| and ||B||, and the angle (in radians) ?_{A,B} between A and B for

A = egin{bmatrix} 2 & -3 \ -1 & 1 \ -2 & -2 end{bmatrix} and B = egin{bmatrix} -3 & -3 \ 3 & -1 \ 2 & -1 end{bmatrix}.

?A, B? =
||A|| =
||B|| =
?_{A,B} =

If A and B are arbitrary real m × n matrices, then the mapping

?A, B? = trace(A^T B)

defines an inner product in ?^m×n. Use this inner product to find ?A, B?, the norms ||A|| and ||B||, and the angle (in radians) ?A,B between A and B for

A = eginbmatrix 2 -3 -1 1 -2 -2 endbmatrix and B = eginbmatrix -3 -3 3 -1 2 -1 endbmatrix.

?A, B? =
||A|| =
||B|| =
?A,B =

Added by Victoria I.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Supreeta N

06/09/2023

Step 1

First, we need to find the transpose of matrix A, which is denoted as A^T. To find the transpose of a matrix, we simply swap the rows and columns. So, for matrix A: A = [-3, 3] [3, 3] A^T = [-3, 3] [3, 3] Show more…

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If A and B are arbitrary real m x n matrices, then the mapping ✈A, B✉ = trace(A^T B) defines an inner product in R^{m x n}. Use this inner product to find ✈A, B✉, the norms ||A|| and ||B||, and the angle (in radians) α_{A,B} between A and B for A = [[2, -3], [-1, 1], [-2, -2]] and B = [[-3, -3], [3, -1], [2, -1]]. ✈A, B✉ = ||A|| = ||B|| = α_{A,B} =