Let A.3 be 5x5 matrices such that det (A) = 7 and det(A)=-3. Find the following (1) det(2(A^B)') (11) det (adj(3))

Q: a) For invertible matrices A, BER"Xn, show that ((AB)")- = (A-)"(B)".

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A: This problem is related to the vector algebra. The problem is solved in the following image.

Q: Suppose A is a 8x4 matrix such that rank(A) = 3. Find dim(col(A)-). dim(col(A)+) =

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Q: Let A, B, C be (3 x 3) matrices, such that det(A) = 2, det(B) = 7, det(C) = 1. What is the value of…

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A: 1.a A=123-111201A=11-0-2-1-2+30-2     =1+6-6     =1determinant of A is not zero, therefore inverse…

Q: (a) If A and C arenxn matrices with C invertible, prove that: det (C-AC) = det(A). (b) Given that…

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Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

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Q: For the​ matrixA=daig(-2,-1,2), put the following values in increasing​ order: det(A),​ rank(A),…

A: Given the matrix A=daig(-2,-1,2) is diagonal matrix Therefore the eigen values of A are -2, -1, 2.

Q: A and B are n x n matrices.    check the true statements below:   1) det(A)det(B) = -det(B^(t)A^(t))…

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Q: For each of the following pairs of matrices A and B, find the products (AB)", A'B", and B'A" and…

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Q: and (96) = C1 A₁-3+4i with ₁ = Write the solution to the linear system [+] in the following forms.…

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Q: -*₁+3x₂ = 2 2x1 + x2 + 4x3 = 3 x₂ + 2x3 = 4 (a) Using [IA]~ [A¹1], Find A-¹. (b) Find Adj A.…

A: note : Since you have posted multiple questions with multiple sub parts, we will provide the…

Q: For the matrixA=daig(-2,-1,2), put the following values in increasing order: det(A), rank(A),…

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Q: Use determinant to find the equation of the line that passes through the points (4, ― 3) & ( ―1,2)

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Q: Let A and B be two 3X3 matrices with det(A)=4 and det(B)=3. Then we have det(A'B²)=9/4. Select one:…

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Q: 3 - 3 1 /- 1

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Q: Let A be 3x3 matrix where det(-A) = 2 2007 let B =030 Then det(A BAB) = L004 Answer:

A: Properties of determinant: det(-A)=-det(A)det(A-1)=1det(A)det(AB)=det(A)·det(B)det(An)=(det(A))n If…

Q: [1 3 B = 2 1 5 0 A = 0 -5 4 and 3 8 QA + B'.

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Q: (2) Let A be 3x3 matrix with 4|| = 4 Find : (a) det(( 3 4 )²(2 4)') ) det( 2 A + 3 adj ( A ))

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