- [ 58. Let A = ²]. 12 34 b a c d ] such that a) Find all matrices B = AB = BA. b) Use the results of part (a) to exhibit (2 x 2) matrices B and C such that AB = BA and AC # CA.

Q: Verify that (AB)T = BTAT.

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Q: Let a and b be real numbers satisfying a² - a -1 = 0 and 6² - 36 - 2 = 0, and let V = 1 a b ab (a)…

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Q: 1 Find the linear combination 2$1 +382 + 4s3 b. Then write b as a matrix-vector multiplication Sx.…

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Q: Which of the following row operations are valid? a)r = 2r1 %3D b)r2 = 4r1 + r2 %3D c)r3 ri ,…

A: Solution: the correct option is (c).

Q: a) If A and B are invertible and their inverses are A¹ and B-¹ respectively, prove that the inverse…

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Q: Express Ac as a linear combination of the columns of A.

A: Given A=2-34-1235-1-2   C=214

Q: Determine whether or not ( ABC )T = C"B"AT for matrices: A, B, C

A: Given- ABCT=CTBTAT To Determine- Whether the above statement is correct or not for matrices A,B,C.…

Q: b) Consider the following matrices: Solution: M₁ = [1 −7], M₂ = [1 2], M₁ = (1 1]. A = [23], B= [13…

A: Step 1: Determine if A is in the set Span({M1​,M2​,M3​}).Step 2: Determine if B is in the set…

Q: (9) Given A = and B = 6 .cCalculate: 3 a) AT b) A+B c) A*B (matrix multiplication)

A: Given that               A=2123       and  B=1-103 Now we find a)AT  b)A+B   c)A*B(matrix…