[10 01 1 10 A = 0 1

Q: Find the general solutions of the systems whose augmented matrices are given in Exercises 7–14.

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Q: Let C be an nxn matrix that satisfies C2 -3C–2In 0. Show that C is invertible and C=1 = }(31-A)

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Q: Consider the following matrix A, where 4 0 -7 0 0 3 -5 2 A = 7 3 -6 4 -8 5 0 2 -3 0 0 9. -1 2

A: A matrix is said to be invertible if it's determinant value comes out to be non-zero.

Q: 5. 23-3 40 6 1 3 5

A: Introduction: The Cofactor is the number you get when you remove the column and row of a designated…

Q: Let (x, y, z) E R³ and the transformation T: R³ → R² be given by T(x, y, z) = (2x + 4y, x + 3y + z).

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Q: Is it possible for A3 to be an identity matrix without A beinginvertible? Explain.

A: To explain:It is possible for A3 to be an identity matrix without A being invertible.By definition

Q: A)  Justify if the matrix A is diagonalizable.B)  Find a matrix T and a diagonal matrix J, such that…

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Q: Find an invertible matrix U such that UA R is the [21 1 -1 -1 0] -12 1 1 A = 3 -1 1-2 3

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Q: 22. 2244 1133 102 1 4132

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Q: Use the eigs () function to check the condition/structure of the XTX matrix

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Q: 7. 1 30 -2 3 1 -5 7 52 -1 2 2 4 1 -3

A: I have explained everything with in the solution. Please go through that.

Q: Exercise 51. Is there a square matrix X with real entries such that det(X¹X) = -3?

A: detXTX=-3 X is a square matrix with real entries.

Q: 4.) Prove that the following statements are true when A and B are square matrices of order n and c…

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Q: -9 4 4 1. Let A = -8 3 4 . Find an invertible matrix P and diagonal matrix D so that A = PDP-1.…

A: See the detailed solution below.

Q: Find an explicit description of NulA by listing vectors that span the null space, where [1 5 -4 -3…

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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: 5. X1 +х2 -3x1 + 2x3 х2 - 2х3 || 0 2

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Q: X = 8 8 3 3 ; A = 2 42 0 1 -2 -3 7 3 3 2 9

A: Every matrix of order m×n is represented a linear transformation from Rn→Rm definition of T(x)=Ax

Q: 7. 1 -2 3 1 30 -5 7 52 1 2 - 2 4 1 -3

A: Given: Objective: To find the determinant by row reduction to echelon form.

Q: In Exercises 5-8, use the definition of Ax to write the matrix equation as a vector equation, or…

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Q: 0 0 1 -1 0 0 -1 2002

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Q: [ 8 }] -7 -3

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Q: "determine by inspection whether the matrix is invertible."

A: Method of inspection tells us that for a Triangular matrix if all the elements of the main diagonal…

Q: 4. Let A be a symmetric matrix. Show that (A' + A) is symmetric.

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Q: 11. 3 5 -6 4 0-2 3 -3 0 0 1 5 0 0 0 3

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Q: 18. A = 19. A: = 0 1 0 0 0010 1000 0001 0002 0031 0212 3 4 14

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