Let A be an n × n matrix over C, then det(A¯) = det(A), where A¯ i,j = Ai,j . Here, z¯ = a − ib when z = a + ib, the complex conjugate of z.

Q: Let A be any m×n matrix, Omn be the m×n zero matrix, and c be scalar. Show that if cA = Omn then…

A: Let A be matrix of order m× n Then A = aij   where i is row and j is column ,   i = 1, 2, . . . m…

Q: Let 2 -1 | -1 2 -1 -1 -1 -1 -1 –1 -1 2 -1 2 be the Eç Cartan matrix corresponding to the simple…

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Q: Let Q be the n × n real matrix in which each entry is 1. Show that det(Q−nIn ) = 0.

A: Given:         Q=11....111....1....................11....1n×n,…

Q: 9. Show that the matrix 0 0 -1 0 0 1 -1 C2 = x, x- will transform the vector y into -y

A: We have to show that the matrix C2 will transform the vector in ℝ3 into the vector -x-yz. First we…

Q: Suppose that A and B are invertible 2 x 2 matrices such that det(AT) = 2 and det(B) = -2. Let x ER…

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Q: Let A be an m × n matrix and r, s E R two scalars. Show the property that (r + s)A = rA + sA.

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Q: Let y = 1 2 and u= 4 2 Write y as the sum of a vector in Span (u) and a vector orthogonal to u.…

A: Introduction: The projection of a vector onto another vector is the application of dot product. This…

Q: Let 1 1 -2 1 2 3 | A = 1 4 and B = -6 -2 -3 - -3 2 1 -1 -1 | Find the inverse of the matrix A + B –…

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Q: Find the change of basis matrix from B1 to B2. -1 2

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Q: 6 -1 Evaluate ABT – 3C given that (2 -2 lo -1 2. -2 A = 6 -3 ‚B = and C = -12 7. 3. Use matrix…

A: To solve the given matrix problems.

Q: Let b₁=(1). -(-9), --(-4), C1 = = (-3). {c₁, c2} be bases for R². Find the change of coordinates…

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Q: 5) Consider the following matrix: A = 1 2 20 -1 1 030 (i) Compute the adjoint of A. (ii) Use this to…

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Q: Let A be a 2-by-2 "symmetric" matrix satisfying the 3 conditions below (where I and 0 indicate the…

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Q: Let A and B be square matrices of order 3 such that |A-| = x + 7 with x + -7 and |A * A" | = . What…

A: A and B are square matrices. Therefore, det(AB)=det(A).det(B) det(A)=det((A)T) We will use these…

Q: True or False: Let A be an n × n matrix over C, then det(A¯) = det(A), where A¯ i,j = Ai,j . Here,…

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Q: Properties of Transpose If r is a scalar and A and B are matrices of the appropriate sizes, then 1.…

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Q: Let I be the 2 x 2 identity matrix. What is det (-41)?

A: The given data is:  I be the 2×2 identity matrix  To find det-4I Given:  I be the 2×2 I=1001

Q: Let -1 1 A = -1 1 -1 -3 3 Find an upper triangular matrix which is orthogonally similar to A.

A: An upper triangular matrix is a triangular matrix with all elements equal to below the main…

Q: 6 X1 -1 -5 X2 II

A: Let us consider the system of differential equation X'=AX then the solution of system of equation is…

Q: Find the adjoint of square matrix [A] 2 [A] = 3 -4 -2 I5 3 1

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Q: Let A = a) Find all matrices B e M2(C) which commute with A. b) Find all matrices B e M2(C) for…

A: We know that  two matrices X & Y commute if  X Y=Y X We are given matrix A. We have to find all…

Q: Let A be a 4x4 matrix and det(A)=2. Find det(2A-)'

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Q: Let A be a 2x2 matrix, c a scalar. Then det(cA)= c*det(A). Select one: O True False

A: Select one: True or false: