In Exercises 29–32, find the elementary row operation that trans- forms the first matrix into the second, and then find the reverse row operation that transforms the second matrix into the first. 1 2 -5 1 2 -5 1 -3 -2 1 -3 -2 0 -3 9. 5 0 0 -1

Q: Find an LU factorization for the matrix A = -2 3 4 1 -3 0 2 3-2, Verify that LU = A.

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Q: Compute the adjugate of the following matrix: 5 60 adj 4 -7 -5 -10 -4 -6 000 000 000

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Q: Express the quadratic form (c₁r1 + c₂2+...+Cnn)² in the matrix notation TA, where A is symmetric.

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Q: Find the transpose of matrix A A = 4 0 -6 3 -8 1

A: Matrix transpose

Q: Find a basis for the row space of

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Q: find the inverse matrix  of 1 1 -4 -2 -1 7 1 -1 -1

A: To find The inverse of the given matrix

Q: Find the nullspace of the matrix

A: By definition , nullspace of a matrix A is the collection of all vectors x such that Ax=0 Given…

Q: t matrix B= 5-21 4-2 what is The 2. 3. 1-12 -12 reduced Yow echelon form of 6 B.

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Q: Find matrix such that 5 3 -1] X+ 2 -3 1

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Q: 8. (3pts) Let A and B be arbitrary n x n matrices. Multiply (A – B)(A+ B).

A: As we know that (A-B)(A+B) = AA+AB-BA-BB=A2+AB-BA-B2here AB need not to be equal to the BA. Because…

Q: In Exercises 13–18, perform each matrix row operation and write the new matrix. -6 4| 10 13. 1 5 -5…

A: In a matrix we can multiple  or divide any row or any column using real numbers . Similarly we can…

Q: Prove that (A + B)² = -(A + B) in matrix..

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Q: NA 1.2) Consider the following new task: 101) Suppose the "N" on the left is written in regular 12-…

A: Step 1: Step 2: Step 3: Step 4:

Q: om: A is a matrix such that A2 + 5A 10. Show that A is invertible and A-1 = A + 51.

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Q: Find a 2 x 2 matrix such that 3 -2 -2 = 61

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Q: Find ∣A−1∣ for the matrix

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Q: Compute the adjugate of the following matrix: -7 3 -6 0 0 0 0 0 0 0 0 0 adj -7 0 -2 %3D | 2 -8 4

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Q: Could a rref matrix look like | 1 0 0 1 | | 0 1 0 1…

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Q: ging %3D

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Q: Q5) Check whether the following matrix is diagonalizable or not. 7 -3 A = -9 -2 3 18 -8,

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Q: is there any way you could write this on paper? or just write the matrix part on paper

A: We have the system of equations as x1+x2+x3=56x1+7x2-3x3=5

Q: 4. Explain what is wrong with the following "proof" that (ABC)" – C"B" A" for three conformable…

A: Properties of transpose of a matrix: (AB)⊥ = B⊥A⊥ Given: (ABC)⊥.

Q: 6. 1 -5 -4 0 3 4 -3 6 0

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Q: Is the matrix A invertible -1 2 3 -6 O True O False

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Q: Write down the (3,3) entry of the inverse of the matrix [1 2 3 122 1 1 1 A

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Q: Diagonalize the matrix [5 -14] 4 -10 A = by writing it as A = PDP-¹ P = D = P-1 =

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Q: 3 5 4

A: Theorem 8: An Inverse Formula  "Let be an invertible matrix. Then Adjugate Matrix: Let be an…

Q: Write Matlab program to find the sum of every row in matrix A: [3 - 4 81 - 3 A = -2 5 6 8. 413

A: % creating the Matrix A A=[3 -4 8; 5 4 -3; -2 1 5; 6 3 -8] A =3 -4 8 5 4 -3 -2 1 5 6 3 -8…

Q: 7. x1 4 -1 7 -4 + x2 -5 3 -5 1 + x3 7 -8 0 2 = 6 -8 0 -7

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Q: Find the power of A for the matrixA16

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Q: Determine all the n × n− matrix A with the range such that A2 = A.

A: Clearly the zero matrix and identity matrix are the trivial examples of our problems. However there…

Q: Explain the mandatory conditions for the addition of two matrices?

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