Part I: Mark each statement True or False. If true, write “T" into the bracket; Otherwise, write “F" simply. (2 points for each question; Full Score: 10 points) 1. (A+B)²=A²+B² is always true for any two nxn matrices A and B. 2. Let H={v|v= (1,x,x,,x, ),x, e R,i = 2,3,*,n}. Then the set H is a %3= ... subspace of R". 3. If vị and v2 are eigenvectors of A corresponding to eigenvalues 1 and 2, respectively, then vị+v2 is also an eigenvector of A. 4. A row scaling on a square matrix does not change the value of its determinant. 5. If AP=PD with D diagonal, then the nonzero columns of P must be eigenvectors of A.

Q: Let A be a m x 3 matrix with columns V₁, V2, V3. Find A0, A (-0. and A 0

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Q: Let x1, x2, x3, and b be the column matrices.Find constants a, b, and c such that ax1 + bx2 + cx3 =…

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Q: Find the solution to the system of equations using Gaussian Elimination - 2y + z = 0 %3| y + 2z = 9…

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Q: Determine whether b is in the column space of A. A = 1. -102 5 8-10, b = -3-3 6 3

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Q: Find the inverse of the matrix: in F7. 2 5 1 1 3 26 3 5

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Q: mark each statement True or False (T/F). Justify each answer.6 (T/F) In some cases, a matrix may be…

A: The given statement, A matrix may be row reduced to more than one matrix in reduced echelon form,…

Q: Find the transpose of each matrix.

A: To find transpose of a given matrix interchange its rows and columns  a. b.

Q: 15 Use Use the Inverse matrix (x-4y=D5 4x -15 y= 20 %3D

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