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(1) For this problem assume that we know the following: If X is an m m matrix, if Y is an m n matrix and if 0 and I are zero and identity matrices of appropriate sizes, then X Y det = det X.
Solution: First observe that if a matrix has dimensions n m then its transpose has dimensions m n. So if the matrix is equal to its transpose, we must have n = m|i.e. the matrix must be square.
Problem #4: Consider the following matrix 1 1 1 1 A = 1 1 Find a matrix P that diagonalizes A Го о (А)| 0 1 0 1 0 1 1 0 1 -1 1 1 -1 1 0 (В) о (C) 0 (D) 0 (E) 1 (F) 0 1 1 1 0 1 1 1 1 0 1 -1 0 1 0 0 1 0 1 1 …
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Problem Find replacements for a, b, c, d so that the matrix has rank of 1. We now consider the nonhomogenous linear system . We first observe that the solutions to the associated …
atic way to solve matrix equations. As we have seen, the vector Ax is a linear combination of the columns of A with the coeffi ients given by the components of x. Therefore, the matrix equation …
Here’s the best way to solve it. Problem #4: Option (A) Solution: Since is a … Problem #4: Consider the following matrix. 1 0 A = 1 0 0 0 0 0 Find a matrix P that diagonalizes A. 1 1 1 -1 1 …
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The Matrix Solution We can shorten this: to this: AX = B where A is the 3x3 matrix of x, y and z coefficients X is x, y and z, and B is 6, −4 and 27 Then (as shown on the Inverse of a Matrix …
A lower triangular matrix is a square matrix with all its elements above the main diagonal equal to zero. Matrix L shown below is an example of a lower triangular matrix.
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