4 8 -12 A--16 -32 49 20 40 -55 Express A in the form A LDU, where L, is lower triangular with 1's along the main diagonal, u, is upper triangular, and D is a diagonal matrix. L,DU =

Q: 2 1 3 Let A be a 3 x 3 diagonalizable matrix, P = 2 1 -1 1 1 1 [2 P-1 = 3 -21, D =10 3 If P-1 AP = D…

A: Given: Let A be 3x3 diagonalizable matrix, P=01231-1-23011, P-1=11030-2-303, D=20000000-1

Q: -2 2 1 Determine if the matrix A = -4 4 2 is diagonalizable. If so, find an invertible matrix P and…

A: Given matrix is A=−221−4421−10. First, we have to find the eigenvalues of A=−221−4421−10. The…

Q: 0. -1 -31 01 2. Let A be a 4 x 4 diagonalizable matrix, P = 0. 0 1 [1 D =0 Lo o 2 01 P-1 = 21 01 1 1…

A:

Q: 3 -3 2 B = 5 1 3 2 -2 -1 e. The elementary matrix E, multiplies the second row of B by 1/6. EEE E,…

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Q: 17 17 Find the transpose of the matrix A = | 14 -2 3 13 14 20 AT = %3D

A: Given the matrix

Q: (1 3 2 3 2 4 Question 3. Consider the matrix A = . Is there an orthogonal matrix P and a diagonal…

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Q: 4. Assume the invertible matrix A satisfies 10 4 2 1 3 1 1 A 4 A -1 -1 A 6 1 -2 3 4 -3 Find the…

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Q: 4. Given the matrix A below,  A = [ 2 1 3           1 -1 1           1 4 -2 ] find  a) its…

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Q: [0 Let A be a 3 x 3 diagonalizable matrix, P =|0 li 1 -3 2 [5 3 D = |0 3 0| P-1 =| 0 Lo -1 If P-1 A…

A:

Q: -5 -8 0 12. Show that the matrix A = 3 5 0 is involutory. 2 -1

A: We can easily check  whether a matrix is involutory or not. For this, check the square of a matrix…

Q: 2 1 -1 3 1 9. Calculate the rank of the matrix P = | 2 1 2 0 3 1 1 1 |-1 -5 -3 -7 3|

A: P=210-131212003111-1-5-3-73

Q: 1 5 Let A = then the Cayley-Hamilton Theorem for matrix A is ... -8 2 A2-3A+42| =0 A2- 2A +40 I = 0…

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Q: -23 16 24 Let A = -6 5 . Find an invertible matrix P and a diagonal matrix D such that D = P-'AP.…

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Q: 2 -6 6. -4 -7 Let A = 3 5 -1 -6 4 -8 8 -3 9. Which one of the following is an LU factorization of…

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Q: -2 5 Find the characteristic equation of the matrix 3 5 C. 22 – 32 – 25 = 0|| D. 2? +72 - 25 = 0 A.…

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Q: -5 2 -2 Show that A E 3 -2 -2 and B 1 -4 are similar matrices by finding an invertible matrix P…

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Q: -9 -9 -42 -36 Let A = and let B = 3. -8 33 15 Solve the matrix equation for X : 3X = 3A –B. ЗА -В.…

A: Divide both sides by 3

Q: 1. (i) What is a rank of a matrix? (ii) Find the rank of the following matrix from an echelon matrix…

A: Use thw definition of rank and echelon form of matrix to solve this problem as in next step.

Q: 2 1 4 6 Find a matrix X that satisfies A(X+I,)=B, where A = and B = 6 5 3 5

A:

Q: 5 7 2) 3 1and B -1-2 0 10 ( 5. The Matrix A and B are a non nxn matrix. Given that A= 2 11( %3D -5…

A: Given that A=572231-1-20 and B-1=100110-5-21 (a) The objective is to find A-1. Determinant of matrix…

Q: 1 -2 0 4 3 18. Calculate the rank of the matrix P 1 1 -1 -5 -1 8 2 -12 3.

A: Rank of a matrix is the maximum number of linearly independent rows of a matrix. The rank of a…

Q: (-1 7 -5 7. Let A = -4 11 -6). Diagonalize A if possible or explain why the matrix A is not -4 8 -3.…

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Q: -5 41 ka) Find rank of matrix A 1 -2 1 -4 5. .

A: We are given a matrix 2-541-211-45 For checking the rank, first let us calculate the determinant of…

Q: 4 -1 5 -2 where I is the identity matrix. Let A = Compute 31 – A and (31)A,

A: To compute the following matrix

Q: 10. (1 2) * Let A: is equal to | and write A as the sum of a symmetric and skew-symmetric matrix.…

A:

Q: [ 2 2 3 4 5. Let A = 5 and b= 0.8 -1.2 -0.3 (a). (10 pts) Find the LU factorization of matrix A.…

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Q: [2 -1 Let A= 5 2 B= 7 4 2 5 C= 3 3 4 8. Find the matrix D such that CD-AB=0.

A: We have given the matrices A, B, C such that CD-AB=0 We have to find the matrix D

Q: 1 If A = a %3D then A is an orthogonal matrix when a. a = ±2 O b. a = ±1 %3D O c. a = ± d. α- +3

A:

Q: [1 2 4] Let S = |2 1 3 be a symmetric matrix. Find the symmetric factorization of S as 4 3 1 S =…

A: We have  S=124213431 It is a symmetric matrix   We have to find symmetric factorization of S as…

Q: 1 0.1 0.9 3 -12 6 Given Matrix A = 4. 1 -5 5 1. 17 6 -2

A:

Q: [ -2 2 Let A = 2 i Find a matrix P that orthogonally diagonalizes A. Then, verify that 1 the…

A: Given that,A=-2221The matrix P that orthogonally diagonalizes A is determined as shown below.

Q: 2. The following matrices correspond to the augmented matrix of a linear system of equations. GIve…

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Q: 1 4 5 Let A = 8 8a -6 . If a = -1 then the rank of a matrix a |1+a? 8a+4 2a+21 A is

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Q: 4 -3 2 Given the matrix A = 5 -2 0 \1/2 3 7 -5/2/ (a) Calculate az31 + a13 and az4 + a24 (b)…

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Q: 3. Let A be an invertible matrix such that A-¹ = NOT 2 0 1 2 01 1 1 Solve the system (2A2)x= b,…

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Q: 5 2 2 5 Let A= 3 -1 B = 4 7 4 3 8 Find the matrix D such that CD - AB= 0

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Q: A 10 x 16 matrix A has maximal rank. What is its nullity? а. 26 b. 16 с. 10 d. 6 е. О

A: Using Rank- Nullity Thereom,

Q: 34 12 25 13 5 30 22 a.) Pivot variables of matrix A? 0 1 1 1 -2 1 1 Let A = b.) Free variables of…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 1 3 0 2 1 0 6. Let A = and B = 5 1 (a) Calculate the matrix Aª. (b) Calculate the matrix B-2.

A: By  using the property  (AB)-1 = B-1A-1

Q: 1 0 1 3 0 2 6. Let A = and B = %3D 5 1 (a) Calculate the matrix Aª.

A: given matrix  A=1051 (a') to find A4 multiply the matrices using matrix multiplication. A4=A2·A2…

Q: 6 5 3 7 7 7 9. a Consider the matrix A = n f 5 4 6 h e Calculate a33 Calculate a13

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Q: [2 0 01 Let A = 1 2 1 lo 1 21 Find two matrices that are similar to matrix A.

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Q: -11 is singular -3] a Q1/A) Find the value of a, where A = 3 -1 -2 a matrix.

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 3 -1 6) If X = is a matrix of order 2x1, given that A= [1 2 B = C = find the matrix X such that AX…

A: Given A=3-112, B=31, C=1-2 and X=pq

Q: 1 1 1' Let A be a 3x3 diagonalizable matrix, P 1 1 p-1- 0 1 2. 0 0 -2 D 0. If P-'AP = D then A2 is…

A: I have explained all necessary information in the solution part

Q: 8 -18 Let A = and let B = 4 %3D 6 16 Solve the matrix equation for X: 2X = 2A-B.

A: Given:

Q: 5 3 Let A=2 -1 8 -7 4 3. 2-1 33 8. Find an elementary matrix E that satisfies the equation EC = A…

A: The Given Equation  is :  EC=A⇒ECC-1=AC-1⇒E=AC-1---(1) Now we will find C-1…

Q: 5 15. Let A be the matrix -3 1 (a) Compute A-!. (b) Use part (a) to find the unique solution to the…

A:

Q: 2 Let A and B be 3 × 3 matrices such that A 3 = B 6. The matrix C = A – 2B is invertibl [5] l10. A)…

A: We want to find C is invertible of not