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: [-3 -2 Let A= 0 -6 and b = 14 3 2 6 Determine whether b is in the column space of A.

A: If b is in column space of A then Rank (A:b)=Rank(A).

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Q: Let X be a 3 x 4 matrix, let Y be a 4 x 4 matrix and let Z be a 4 x 3 matrix. Select all of the…

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Q: Product of matrices multiplication A=[a, b; c, d] x[1,0;0,1]

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Q: ? 3x1 – 2x3 4x1 х — Xә + хз X1 ? ? ? X2 ? ? ? X3 ||

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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: Let A and B be n x n invertible matrices. Use matrix algebra to simplify A(A¯¹ + B¯¹)B.

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Q: , and c

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Q: Find the inverse of each matrix. 3 26) 0.

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Q: = [₁ Construct a 2 x 2 matrix B such that - AB is the zero matrix. Use two different nonzero columns…

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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…

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Q: State whether or not the matrix is in reduced form. 130 1 0 0 10 0001 Not Reduced Form Reduced Form

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Q: Find the transpose of each matrix.

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Q: Find the relation determined by the diagraph and give its matrix

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Q: II. Find the inverse of each matrix. -9 6 2. 4 -8

A: Let    A=-964-8 We have to find its inverse. We have several method now we use elementary row…