[2 4. Compute the inverse of the matrix A = 3 5 5 in three ways: 1 89 (a) Using the adjoint formula above. (b) Using a cofactor expansion along row 1. (c) Using Gauss-Jordan elimination to reduce A to the identity matrix 13.

Q: Q.7: Find A and X to diagonalize the following matrices B1 and B2: B, = 108 [0.6 0.91 !0.4 0.1) [0.6…

A: first we will diagonalize each matrix and then with the help of diagonal form we can calculate Bk

Q: Let M [1 -2 -4] 7 -1 3 Perform the first step in Gaussian elimination by taking a scalar multiple of…

A: The given matrix is .The objective is to find the row echelon form of the matrix.

Q: Suppose that A = Determine the elementary matrices and their inverses based on the following…

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Q: 2. For the matrix 2 2 -1 B -3 3 find its Pseduoinverse Bt and the 2-norm ||B*||2.

A: Given : B=212-1-1-3-13 To find : pseudoinverse B+ and the 2-norm ∥B+∥2

Q: Prove the following properties of matrix addition and scalar multiplication, where A, B, and C are…

A: Use the properties of matrices to prove this statement.

Q: Assume the following matrix is given Be when x = I I I X 1000 000 1 00 1 0 where x is any non-zero R…

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Q: Consider the matrix 1 4 A = 2 3 (a) Compute A-1 (b) Find det(A-') (c) Deduce a relation (if it…

A: Given the matrix A = 1423 a) compute A-1 A-1=1Aadj A adj A = 3-4-21 A = 3-8 = -5…

Q: (24)*. Use the inverse matrices to find АВ and 1 3 1 4 2. 4 2 1 A-1 = B-1 = 2. 2 2 4 1 -2 2 4 -1 (a)…

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Q: 1. b) Find the Inverse of the matrix 1 2. 1 using Gauss-Jordan method. 1 1. 2]

A: Augment the given matrix with identity matrix. Apply row operations to convert given matrix into…

Q: Find the RREF of the matrix 2 3 12 -2 22 -2

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Q: Consider the following 2 x 2 matrix -5 A = 3. For any matrix, we have a clear understanding of some…

A: Given the matrix: A=−536−2 (a) To calculate the eigenvalues and eigenvectors of A.

Q: 4. Consider the matrix A= = 1 1 2 3 1 2 3 -4 -5 1 1 3-4 4 -5 8 Find the determinant of A via…

A: The solution is shown below- As per bartleby guidelines only first part is allowed to solve. Kindly…

Q: I need to prove each of the following, showing all steps.

A: Prove the following (a) Let A and C are symmetric matrices, then . (b)

Q: A = -1 1] 2 1 2 3 (a) Calculate each of the cofactors C₁, of the matrix A. (b) Use cofactor…

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Q: 2.1. Prove that B Is erse of A -17 11] -7,B: 0 3 2 [1 1 2 2 4 -3 [3 6 -5] 2 A = -1 11

A: To prove that B is the inverse of A.

Q: [101] Find the inverse of the matrix C = 0 1 1 using cofactors. Show all your work. L2 1 4]

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Q: 9. (a). Suppose A is an (nxn)-matrix over the complex numbers satisfying A² = I. Show that A is…

A: What is Minimal Polynomial: A minimal polynomial is related to as square matrix. It is the…

Q: 3. Let A - 3202 3219 3 3 0 5 0 -2 -3 0 2 10 3 2 Evaluate det(A) by a cofactor expansion along a row…

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Q: 1. (C"B)A" 3 A = -1 B = -1 4 C = 1 2. tr(4ET – D) 1 1 1 2 6. 1 3 D = -1 1 E = -1 1 3 2 4 4. 3

A: To evaluate the given matrices.

Q: 6 -4 For the matrix A find a matrix C such that C-1AC is in canonical form and 1 state the canonical…

A: Given matrix is A=6−412. We have to find he matrix C such that C−1AC is in canonical form and state…

Q: [1 Q6/ Find the matrix inverse of B = 3 L2 4 07 1 1 1 21

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Q: 3 1.2 Given X = =[-³₁₁³] and Y = [-23 19]. 0 show that (X-Y)(X+Y) # x² - y²

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Q: 3. Diagonalize the following matrix. Use this diagonalization to compute A¹⁰ 1 А A = [¹₁2] 2.

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Q: For each 2 x 2 real matrix A find the canonical form B and an invertible matrix P such that P-1 AP =…

A: A square matrix A of order 2x2 is said to be diagonalizable if there exist an invertiable matrix P…

Q: 1. ²²(²5 3) ` = [(-3³ -¯2)] a[; Find x such that 2

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: 4 8. 5. Let C = 0. the cofactor matrix of a matrix A and let 7. -7 9] 611 b12 b13 A the inverse…

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Q: Let A =mnd B- then the matrix (2AB + A")" is equal to O None of these O equal to the above 2 17

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Q: (a) What is the 2 x 2 matrix M that reflects v = ( 7 ) to ( ² ) ? y for M-1 makes sense…

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Q: (d) Is the matrix [2]12 [112] [-112 [2]12 a unit in the ring M2 (Z12)? Justify your answer.

A: (d)

Q: 1. 2. 3. Given A = 3 -1] 4 7 Given X = and B= 1 -2] [10 31 Show that (X+Y)(X-Y)# X²-Y² 1 [ and Y= 1…

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Q: Use the adjoint method to determine the inverse of the coefficient matrix given by [2 3 1 A=3 4 1 l3…

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Q: 4. Consider the same function f(x) = xe" again. Now, we are going to find the interpolating…

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Q: For the following quadratic forms (i) write down the symmetric matrix A (so the form is equal to…

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Q: 2. For the matrix A = 2 [1 a) det (A) b) tr (A) c) [1 2 5 Inverse of A 3] 3, calculate 0 81

A: