1. (a) The matrix I = is called an matrix. (b) If A is a 2 x 2 matrix, then A X I = and IXA = (c) If A and B are 2 x 2 matrices with AB = I, then B is the of A.

Q: Let A be a 5 x 5 matrix with det(A) = -10. 1. If the matrix B is obtained from A by adding 4 times…

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Q: Give an example of a 4 x 4 matrix that is symmetric, has with the (2,4)-entry equal to -5, and has…

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Q: Suppose that 60% of the people who own a GM car buy a GM car for their next vehicle. Also, suppose…

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Q: If A is 4x4 matrix with det(A)=10, find det (24-¹A), det (A²).

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Q: 20. The following are rules of transposition of a matrix except: (explain) a. (A")" = A b. (A + B)"…

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Q: Let A, B be  matrices of the same order. Then det(A+B)=det(A) + det(B).  True or false

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Q: Q2. For the matrix, A = (a) Find 2 Tr (2 A). (b) If A = 21 8 7 4 6 7 5 4 find (A)-².

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Q: Ei) dim(COLA) is (ii) dim(ColA)- is (ii) dim(RowA) is (iv) dim(RowA)- is (v) dim(NulA) is

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Q: Let A be a 3 x 3 matrix, and B be a nonsingular 3 x 3 matrix, such that det(A) = 12 and det(B¹A)=…

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Q: Let A and B be 3 × 3 matrices such that det (B) = -2 and 27 = det (-3AB A" B ²). 2 Find det(A).…

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Q: True or false. Please explain your answer. Let A and B be two nxn matrices. a) b) c) d) If B is a…

A: Let A be a mxn matrix, To Check and explain: whether the following statements are correct or not.…

Q: 3 4 Let X and Y in the set of 2 × 2 matrices, M22. %3D -11 2 3 Determine whether A = or B are in…

A: Given  X=2-121, Y=34-11 and A=0-1181, B=2312

Q: 1 2 -4 -8 (b) -2 -4, 8 16 This set is

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Q: You are given the following matrices: P = (-3 9/-3 -7), Q = (-2 1/3 3) Find out the value of a of…

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Q: Let A be a 3 x 5 matrix in which not all entries are zero. (a) What size must the matrix B be for AB…

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Q: 3. Tell whether the statement is true or false. If true, provide a proof. If false, provide a…

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Q: 2 1 0 0 0 2 0 1 3. Let A and Ba 4 x 4 matrix with det(B) = 3. 0 3 1 -1 2 0 1 (a) (3 marks) Find…

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Q: Suppose that B is a square matrix with det(B) = -2. Find each of the following. (a) det(B6) = (b)…

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Q: 3. Let A, B € Mnxn (F) be n x n matrices. (a) Prove that tr(A + B) = tr(A) + tr(B). (b) Prove that…

A: Trace of matrices is sum of its  diagonal entries

Q: (18) Does a 2 × 2 diagonal matrix commute with every other 2 × 2 matrix?

A: We have to check

Q: Q1. (b) Determine whether the statement is true or false, and justify your answer. (a) The product…

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Q: -4)· (- 1 2 -4 1 -3 2 1 17 -31 (d) -2 -4 16 16 9 10 -8 e? This set is

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Q: 3) Consider the following matrix: A= 020 100 0 4 1 - 1 - 1 (i) Compute A™ ¹. (ii) Write A as a…

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Q: If A is a 3 x3 matrix and det(A) =-3, what is det(4A)?

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Q: Let A and B be two matrices innRREF , if they are row equivalent then A=B.

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Q: Let matrix A = 1 1 1 3 2 1 −2 3 1 (a)Find two distinct row echelon forms of A. (b) Find the…

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Q: ebra to show that for n x n matrices A,B,C and n x 1 vector rtible and ABC then the matrix equation…

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Q: If A is an m x p matrix and B is a p x n matrix, then their product AB will be?

A: Two matrix can only be miltiplied if number of column of first matrix is equal to number of row of…

Q: Let A, B be 4 x 4 matrices. Find two matrices so that rank(A) = rank(B) = 2 and rank(AB) = 1. A = B…

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Q: Express the following invertible matrix A as a product of elementary matrices: You can resize a…

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Q: If matrix [A] is a 5x5 matrix and a matrix [Z] is obtained by the row operations of replacing Rowl…

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Q: If A and B are nXn matrices, then (A-B) =A-2AB+B Select one:

A: A-B2=A-BA-B=A2-AB-BA+B2