16. Matrix Properties. Consider the following matrices: 2 0 5 0 1 1 -2 A = 3 1 -1 B = 2 3 -1 C = 3. -1 2 1 -2 3 4 1 Verify that (a) A(BC) = (AB)C (b) (AB)" = BT AT (c) A(B+C) = AB+ AC

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A:

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Q: Find the characteristic equation of the matrix: 4 C = 2 -2 2.

A: Characteristic equation of the matrix C is given by  det ( C - λI ) = 0

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A: a--False b--True c--False d--True

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Q: 6. (a) Find the matrix A so that AB=C, where C1 C2 C3 b, b, bz 2 B= b, b2 b3 & C= C1 C2 C3) а, а аз…

A: AB=C

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A: Solving Part C only ..as you have already mentioned :-

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Q: If A is a 4×6 matrix and the dim Nul A​=3,what is dim Col A​? Justify your answer.

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Q: DEMONSTRATE THAT A A-1= A-1A = I      FOR THE MATRIX BELOW     1 -1 2 2 -3 4 1 0 3

A: Given matrix A=1-122-34103 We have to  prove that AA-1=A-1A=I We know that A-1=AdjAA

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Q: Let A and B be -1 0 10-3 A = 10-3 -1 0 2 1 2 1 2 2 Find an elementary matrix E such that EB = A.

A: Given that: A=-10210-3122B=10-3-102122

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Q: 3 2 2 3 1, find the matrix B Such that AB = 5 3 4 3 4 2 1 6 1 5 6 4 , If A = 1

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Q: True or False? Suppose that A is any n x m or n xn matrix, then the matrix A'A will be the transpose…

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Q: -3] Let A be a 4 x 4 diagonalizable matrix, P = |–1 1 1 0 2 1 [1 01 P-1 D = |0 Lo 2 1 3 If P-1 A P =…

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Q: Q.1 Consider the following matrix (-1 3 0Y A = 2 0 2 2 1 4 1 B- 2 -1 5 -3 0 1 10 C-2 A. Show that a.…

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Q: 2 0 0 3 -2 0 1 -1 Consider matrix A = -7 2 4 -2 0 0 5 Calculate det (A³) 1.

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Q: Given the matrix below and its corresponding rref(A) and rref(A') 10 0 0 -2 8 -1 -3 10 0 0 0 0 10 0…

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Q: [1 Find a matrix A = -4 -51 = l3. y] 1 z such that A² 10 %3D Lo 1. Lo

A: Given A=1xy01z001 A2-0-4-50010000=I3 To find Matrix A:

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A: As per guideline we have to solve only three parts

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A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: If 4 [a] is a 3x3 matrix, such that ay i (2m-j) then the diagonal elements are

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Q: Ruèstion 12 If A, B and C , are matrices of order 4x3, 2x2 and 3x2 respectively, then the order of…

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Q: 4. The adjoint of the matrix A=1 2 0 3 1 is b. -1 10 0 -15 -2 4 -1 -1 -5 -2 d. Sone of these c. -1

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Q: 1 0 1 3 0 2 6. Let A = and B = %3D 5 1 (a) Calculate the matrix Aª.

A: given matrix  A=1051 (a') to find A4 multiply the matrices using matrix multiplication. A4=A2·A2…

Q: 0 11 0 2 1 5] 3. 2- Find A. A-1 if the matrix A is given by: A = -1

A: As per our guideline we are supposed to answer only first asked question.kindly repost other…

Q: 8. Given the matrix B = |1 1 1 1 1 1 Which of the following matrices solves X in the matrix equation…

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Q: 3 0 1] 0 2 1 5 2- Find A. A-1 if the matrix A is given by: A =| 0

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Q: 1. Use matrix inversion to solve for x, y, and z if: x + 2y + 2z = −1 y − x − z = 0 2z + 3y + 3x = 1

A: see below the answer

Q: 1 4 [5 0 lo 4 -3] b) Given D = -2 3 1 -2 1 85 72 -54] A =| 50 32 -24. -35 -24 18 Find a matrix BT ,…

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Q: Suppose A, B, and X are invertible 3 x 3 matrices. Suppose that [1 2 0 0 1 1 1 3 • A8 = I3; and…

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Q: 2 Let A and B be 3 × 3 matrices such that A 3 = B 6. The matrix C = A – 2B is invertibl [5] l10. A)…

A: We want to find C is invertible of not