1 4 If L= ,U = are factorization of a square matrix A, where L is lower triangular matrix and U is upper triangular matrix. then matrix A = ... -13 O[ 10 3 -1 -1 of 2 8 -1 -1

Q: [5 Consider matrices A =9 -11 11 and B =|0 -1] Two elementary matrices -4 c) 2. 8. 4 1 -1 3 -4 2. E…

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Q: 1. Identify the two-by-two matrix with matrix elements a;; = ij. %3D 1 4 4 2 4. O (1 4.

A: NOTE: Refresh your page if you can't see any equations. . there are 4 elements in the 2*2 matrix,

Q: 10. From Gaussian elimination, one obtains M3M,M, A = U, where U is upper triangular. If A = LU,…

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Q: 7. Suppose that A is an invertible matrix and AB = I, Then (a) Show that BA = I, and (b) And the…

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Q: 1 1 Given that matrix P=|1 0 |0 -1 2 1 , find the matrix A such that -2 0 0 P'AP=| 0 -2 0 0 4

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Q: 1 -14 -9 Find the rank of the matrix 03 01 O2 04 4. 3. 4.

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Q: -12 Find the PA = LDU factorization of the matrix A = 6 -24 13 2 5

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Q: 2 7 Which of the following is the matrix C that satisfies the equality (c" +312) 1 4 -1 3 (a) 2 -5…

A: We have to find matrix

Q: -1 -[::] Determine the dimensions of Nul A and Col A for the matrices. A = 4 7.

A: Before finding the column space or null space, we will reduce the given matrix to its reduced…

Q: 1 u, where u = Compute n.n 1 %3= n.n (Type an integer or simplified fraction for each matrix…

A: We have to solve given problem:

Q: Гз - 12 Find the PA = LDU factorization of the matrix A = 6 -24 13 2 5

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: 8. A square matrix P has a property that P² = P. If P# In, which of the following is true? (a) P is…

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Q: - 10 -20 Let A = 10 22 -10 Find an orthogonal matrix P and a diagonal matrix D such that D= p" AP.…

A: Hope you know how to find eigenvalues and eigenvectors of a matrix. I am not showing the steps to…

Q: 1. Find the Matrix product AB, if it is defined . - [; ㅎ 3]. 0-| 30 A = -3 1 0 5 A) B) -9 O 25 -12…

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Q: 3 21 3. The all values of a and B, so that the matrix 4-3 1 4 is positive definite, are [2 B 2] (b)…

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Q: [1/V14 2/7 2/V14 -4/7 1//21 5/7 [3/V14 2/7 -2//21 [1 4 8 4//21 [14/V14 28/V14 28/V14 20 1 A : 7 = QR…

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Q: 13 () 9. If A is a 3 x 3 matrix such that A 1 and A 4 1 then the product A 7 is %3D %3D 8

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Q: 1 A = )Find the rank of a matrix 7 17 1 - 2 | 3.

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Q: ' 1 2 3 What is the rank of the matrix A = -1 1 3 0 -1. O 2 O 3 O 1

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Q: 14. If A is a 2 x 2 matrix, its column space contains and its null space contains then: A. A = 5 B.…

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Q: 6 1 .one factorization is P 2 3 2 A factorization A= PDP is not unique. For A= D and p-1 Use this…

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Q: 2 3. 1] Given that matrix P =0 2. Find the matrix A such that A = PBP 1, where 1] -1 1 -2 0 01 B is…

A: Given:The matrix P=2310-12101 , B=-200030006To find:we have to find the matrix A such…

Q: 16 21 Let A = |-14 -19 Find two different diagonal matrices D and the corresponding matrix S such…

A: Given matrix is A=1621-14-19 We find the eigenvectors. For eigenvalues, A-λI=0⇒1621-14-19-λ…

Q: 6. Which of the following is the elementary matrix that multiplies the third row of a four-by-four…

A: We find which of the given is the elementary matrix that multiplies the third row of a four-by-four…

Q: 3. Write an example of matrices B, A such that A is k x n and B is n x k for some positive integers…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: -4 9. 15 Show that A = -1 1 and B = 3 are similar matrices by finding an invertible matrix P…

A: A matrix A is similar to another matrix B when their determinant is the same, their characteristic…

Q: -7 14 -15 -3 -8 [D] = 8 12 16 0 - 16 -17 If matrix [D] has element dre 8, what is r and c? r = and c…

A: Given a matrix of 4×3  and a element given drc = - 8   then we have to find out the value of r and c

Q: 10. Which matrix below is NOT in row echelon form? (1 0 4 4 1 06 0 (A) 0 1 00 0 0 1 0 1 03 4 (C) 0 0…

A: We know that in row echelon form the leading entry of each row is one, but here in B) the leading…

Q: .15 The matrix A %D is an orthogonal matrix. True O False O

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Q: 5.12 Given A = I 0 0 1 0 0 0 2 3 4 S/ find a permutation matrix P, a unit lower triangular matrix L,…

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Q: 17 Let A = -30 -8 Find a matrix S, a diagonal matrix D and S- such that A = SDs-1 -1/2 -1/3 S = D =…

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Q: 8: [1 The matrix A = 4 L3 O True O False -2 31 1 -1 - 2 is a positive definite matrix. 21

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Q: 1 Given the matrix P Find the ( 2, 2 ) entry of P². O 25 9. O 16 4 1 O None of the others are…

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Q: Г1 2 а] Consider a 3x3 matrix P=| 0 1 2, and an another matrix 0 0 1| Question Q= 4; such that P² –…

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Q: 24. Let a matrix B is defined as [2 1 -1] B = 3 2 -3 L3 1 -2 Find, a) a nonsingular matrix P such…

A: The given matrix is: B=21-132-331-2

Q: 8. A square matrix P has a property that P2 P. If P # 1,, which of the following is true? (a) P is…

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Q: 3.4. A square (n × n) matrix is called skew-symmetric (or antisymmetric) if A" = - A. Prove that if…

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Q: 1 2 adj of matrix A= 3 4 Select one: a. 4 2 -3 1 O b. 4 -2 -3 1 O C. 4 -2 -3 -1 O d. 4 2 -3 1

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Q: (17) (a) Consider the following matrix a 1 = ( 4 ) A For which values of a and b is true that A² =…

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Q: 14 12 (suppose) A = – 20 17] Find the diagonal matrix D where D= P¯' AP

A: The given matrix, A=-1412-2017

Q: 9. A matrix raised to the 5th power is the matrix multiplied by itself five times, and the trace of…

A: We will find out the required value.

Q: 28. a. If A is a 3x5 matrix, then the rank of A is at most Why? b. If A is a 3x5 matrix, then the…

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Q: [31 1 Consider the matrix B= 1 3 –1 (adjB)™= 2 4 1 7 -3 -2 1 -10 -4 4 8 7 3 -4 -3 1 4 -2 -10 8 [з1 1…

A: The Adjoint of a matrix is the transpose of its cof-actor matrix. And the transpose of the transpose…

Q: 3.9. Let a matrix B is [1 -21 B = 13 Find B6 by using a nonsingular matrix P such that D = P¯'BP is…

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Q: 8. (i)Redo: For what type of square matrices A will the algebraic system Ax = 2x have solutions…

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Q: 1 6 Suppose that A = 2 and B = 4 1 *| If l is the 2 x 2 3 2 dentity matrix, then compute (A + /)B.…

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Q: 6.7. Which of the following pairs of matrices are unitarily equivalent: 1 0 0 1 a) ( and 1 1 1/2 1/2…

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Q: 9. If M = 2e -Ze-is Is a fundamental matrix for X' = AX, then the exponential matrix et is 2e-…

A: Column of the Fundamental matrix are the solution of the homogeneous differential equation.

Q: If L = 2 07 1 4 ,U = are factorization of a square matrix A, where L is lower triangular matrix and…

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