Consider the matrix A given by 4. -5 3 6 -6 6 5 A = 9 3 -3 0 2 -4 Using elimination, find a lower triangular matrix L and an upper triangular matrix U such that A = LU. Explain the relation ship between L and the elimination matrices used.

Q: Find the elementary matrix E such that EB = A where 2 -12 2 1 1 A = 4 0. -2 and B = 24 %3D | 6. -8 3…

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Q: Suppose that A (A, then det(B)- Select one: A. 15 OB. 5. OC -15 ODO th ) is a (4 x 4) matrix, where…

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Q: Find the matrix D such that ADB = C and hence evaluate f(D-1) given that 4 -2 3 1 6. -6 6:2), c = (6…

A: d2+4d4=6⇒2d4+4d4=6   (d2=2d4)=6d4=6⇒d4=1⇒d2=22d2+8d3=8*2…

Q: Find a 3 x 3 matrix A with the following property: if T(x) = Ax, then the range of T is the…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: If A and B are similar, then there exists a matrix P such that B = PAP. Use this fact to fi -2 2 -3…

A: Here we have to find B5 ,   We have to find if A and B are similar or not, if A and B are similar…

Q: For the matrix A, find (if possible) a nonsingular matrix P such that P-'AP is diagonal. (If not…

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Q: Let A be an 8 x 8 matrix with det (A) = -2. Let B be the matrix that can be obtained by applying the…

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Q: (b) Write down a possible matrix A such that when we apply the above elementary matrices, we get an…

A: Given: The 3 by 3 matrices that produce the elimination steps. E21 subtract 4 times row 1 from row 2…

Q: Give the value(s) of a for which the columns in the matrix 9 6 -6+a A= 6 12 -6 -6+a -6 are linearly…

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Q: determine whether the given matrix A is diagonalizable. Where possible, find a matrix S such that…

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Q: Find the LU factorization of 3 -1 1 A -3 -6 12 8 20 vrite A = LU where L is a lower triangular…

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Q: Find the matrix E so that EB=C, where |1 a2 az 0 B2 B3 a1 a2 dz B= b, b, b, & C= |C1 C2 C3 with a,+0…

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Q: Determine whether the given matrix A is diagonalizable. If so, find a matrix P that diagonalizes A…

A: Given matrix A=01-12 and A=200121-101To find: A matrix P that diagonalizes A and a diagonal matrix…

Q: Which of the following is the LU-factorization of the matrix a) 1 b) 0 1 1 c) d)

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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

Q: Let A be a matrix of order 3, such that -11 13 17 Adj(A) = 1 -23 13 17 9 -19 If F2 = ( 3 -1 2) is…

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Q: determine whether the given matrix A is diagonalizable. Where possible, find a matrix S such that…

A: Consider the given matrix, Find the eigenvalues of matrix A. λ1=4,  λ2= i, λ3 = -i The eigenvector…

Q: If A is a skew-symmetric matrix of order 5 then adj(adj(A5«5)) = %3D

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Q: 9. . Suppose that A = PDP¯' and B = 31 + 2A + A². 5 Let D a Find a diagonal matrix D1 such that B =…

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Q: - 2 Determine det D, adj D and D for the matrix D = 1 2 3 - 2 -1 -2 3

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Q: If the n x n matrices A and B are symmetric and B is in- vertible, which of the matrices in…

A: (16) Given:- A and B are symmetric  ⇒AT=A,    BT=B B is invertible ⇒B-1 exists To prove :- A+B is…

Q: b) If C is an orthogonal matrix and D = C + C-1 show that D is a symmetric matrix.

A: We have to show D is symmetric.

Q: Are the two matrices similar? If so, find a matrix P such that B = P-'AP. (If not possible, enter…

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Q: Find matrices P, D and P-1 that diagonalize matrix A, where A = P = D= P-1 20 0 -11 -2 -3 -30 -1

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Q: -1.T If A is 3x3 nonsingular matrix such that AA' =A'A and B=A A' then BB' = Select one: (B*," b. в…

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Q: (a) The matrix ( (AB)-1 )T comes from (A-1 )T and (B-1 )T In what order?(b) If U is upper triangular…

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Q: Find the LU factorization of 4 4 -1 4 A = -12 -10 -9 12 16 -7 14 That is, write A LU where Lis a…

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Q: Let 2 -1 A = 1 -1 0 2 Find an orthogonal matrix P and a diagonal matrix D such thatt D = P"AP. D =…

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Q: 3.3. Let a matrix B is B = [, В -2 3 Find B6 by using a nonsingular matrix P such that D = P¯'BP is…

A: B=01-23 Characteristic equation of B is given by  λ2-trBλ+detB=0 where trB, detBdenotes the trace…

Q: Let B = {b1, b2, b3} and C = {c1, c2, c3} be two bases for R3 and let the following be true:…

A: Given B = {b1, b2, b3} and C = {c1, c2, c3} be two bases for R3  we need to find the change of…

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 =…

A: Given A be a 4×4 diagonalizable matrix. And given matrix is P=00−3−110102, D=100020002 and…

Q: determine whether the given matrix A is diagonalizable. Where possible, find a matrix S such that…

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Q: Find all a and 3 > 0 so that the matrix B = 23 6 2 is 2 ally dominant:

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Q: Find an elementary matrix E that satisfies the stated equations. 8. 1 5 8 5 8. 1 5 B = 2 -7 D -6 21…

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Q: Consider the matrices A = 1B = ; J, c = ; =G [5 2 K, = l, K2 =L0 3 Solve AX + BY = K, CX + DY = K,…

A: Given matrices A , B , C and D. Matrix K1 and K2 are also given. We need to find matrices X and Y.…

Q: 3. Consider the following matrix: -31 A = |-3 -4 -1 -2 3 2 9. (a) Verify that A is diagonalizable.…

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Q: Which matrix is of the reduced echelon form? Oa. (1 2 04 0 0 2 7 Ob. 1 2 5 0 13-7 10 1 0 0 0 01 0…

A: To find the reduced echelon form of given matrices.

Q: decide whether or not the given matrix A is diagonalizable. If so, find an invertible matrix S and a…

A: Consider the given matrix: Here the objective is to check whether the given matrix is…

Q: Given the matrix 2 22 A = 0 2 3 7 7 1 Find the |A| by transforming the matrix A to the triangular…

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Q: 2] find 1 -1 3 - If A = and B 1 |3| -2 (а) ЗА — В. - (b) The matrix X such that 3A – B+ 3X = 0. ||…

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

Q: Find a matrix C such that A = CB for the matrices 1 4 5] A = |-2 0 1 3 1 0 -4 0 2] B= | 1 4 5 5 5…

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Q: If the product M = ABC of three square matrices is invertible, then B is invertible. (So are A and…

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Q: If a and b are the matrices of order 3 and (A)=5,(b)=3 then find the vailue of 3ab?

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Q: Use the reduce echelon form "triangle upper matrix" to find the det(A), where A = 2 -8 6 8 3 -9 5 10…

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Q: For given symmetric matrix A, find a diagonal matrix D that is congruent to A.

A: Given :      Symmetric matrix A   To find:           A diagonal matrix D that is congruent to A.

Q: Given the matrix 2 2 2 3 1 A = 0 2 7 7 Find the |A| by transforming the matrix A to the triangular…

A: Given :A=222023771

Q: C be the matrix defined as a₁ an C = a-1 9₂ az az a a₂ a, a az a4 1 A an an-l an-2 a₁

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Q: Let B = {b1, b2} and C = {c1, c2} be two bases for R, where %3D bị b2 C1 = C2 = 8 b1 what is the…

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Q: Let A be a 3 x 3 matrix such that det(A) = 12. Suppose B is obtained from A by applying the…

A: We have to find the  det(B).

Q: Give the value(s) of a for which the columns in the matrix 8. -4 4 A = -4 +а 5 -6 4 -6 10 + a are…

A: We will find out the required values.