Give matrix A = (2  -1)                           (3     5).  and that h(T) =  and that h(T) =T² - 2T – 7, find h(T

Q: • The Matrix B from 3 x 2 at by = 1- is 1. 3. 4. 1 -2

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Q: Find A by transforming the columns of the identity matrix, e, and ez. 1 0 1 12 0 1 e1 e2 1 Reflect…

A: The transformation matrix A is, 0 1 1 0

Q: At Compute the matrix exponential e for the system x' = Ax given below. x₁ = 37x₁ - 36x₂, x 2 = 34x₁…

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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: For which value of x is the following matrix not invertible: 1 1 3x A = 3x 3x 3x 3x 3x O 2 4 O1/3 1

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Q: Let A be a 3 x 3 matrix such that A3 - 6A² + 4A – 31, = 0. Then, A is invertible and A

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Q: Solve for the matrix X if AX(D+BX)~' = C. Assume that all matrices are n X n and invertible as…

A: Given that AXD+BX-1=C Pre-multiply by A-1 A-1AXD+BX-1=A-1CXD+BX-1=A-1C post multiply by D+BX…

Q: Find values for the variables so that the matrices are equal.

A: Given that the matrices are equal. x4=6y

Q: 2. (a) Express -2+t+t +r' as a linear combination of 1-t, 1+r, and 1+1- or show that it cannot be…

A: We have to write in the linear combination.

Q: Consider the following matrix A, where 0 -4 -6 0 -3 A = -1 1 2 5 Find an invertible matrix P and a…

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Q: Consider the system X'(t) = | x(t),t > 0. If the eigenvalues of the coefficient matrix are r= -1 and…

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Q: 1 : Find the inverse of the matrix 1 -1 0 A = 3 -1 2 with using the method of Cofactor (Adjoint).

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Q: Find the symmetric matrix A associated with the given quadratic form. 2x2-3y2-z2-4xy

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Q: Let a matrix '2 -2 1 A 2 3 1 1 -2 - 2 2 Show that A"A = I and deduce that AT = A-1.

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Q: For the matrix A , use the Cayley­Hamilton Theorem to compute A -1 and A -2 by expressing each as a…

A: According to Cayley Hamilton theorem, any square matrix satisfies its own characteristics.

Q: Solve for the value of x from the given matrix: [(x - 2) y (2z − j)] = [(y+z) j2 (x-1)]

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Q: Evaluate the determinant of matrix det(A), where 1 1 1 ... X2 T3 In ... A = ... n-1 „n-1

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Q: Tis a linear transformation from R² into R² as shown below. The standard matrix for T-l is T'x, у)…

A: According to the given information, Let T be a linear transformation from R2 into R2 as:

Q: If the determinant of a 5 x 5 matrix A is det(A) = –10, and the matrix C is obtained from A by…

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Q: ve that for every matrix A, (AT)T = A

A: We have to prove that transpose of A transpose is A.

Q: Given a 3x matrix in terms of scalar c and that det (A)=8, find the valuddof G if -1 1c-2 C+7 3. 2.

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Q: Let A be an n xn matrix and B= A+ I, where I is the identity matrix, then it is possible for A and B…

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Q: Find the characteristic equation for the matrix 2 (13). and use it to compute M-¹. M

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Q: In the Attached Problem, show that the matrix A is nilpotent and then use this fact to find the…

A: Given A=1-11-1

Q: If a 4 x 4 matrix A with rows v₁, U₂, U3, and 4 has determinant det A = 9, 5v₁ + 20₁ then det V2 U3…

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Q: Find the matrix exponential eAt for 1 2 A 0 3 By using eAt you have found in part (a), find the…

A: Consider the given matrix.

Q: For the quadratic form x²+ xz - 6yz = 0 in the matrix notation X'AX the matrix A is: 1 1

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Q: 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x? + 2y2 + 2z2 - 2xy- 2xz -…

A: The objective is to find the symmetric matrix and diagonal form of the quadratic form…

Q: For square matrix A, if its first row equals 5 times the third row, then its determinant is 0. True…

A: We are given with the matrix who is first row is five times the third row and we have to find the…

Q: For which value of x is the following matrix not invertible: 1 1 2x A = 1 2x 2x 2x 2x 2x 4 1 -1 1 2

A: For a matrix A to not be invertible: dat(A) = 0.

Q: 2 : Find the inverse of the matrix 1 -1 A = 2 -() 3 1 with using the Cayley-Hamilton theorem.

A: The Cayley Hamilton theorem states that every square matrix satisfies its characteristic equation.…

Q: Let A be the matrix a- [}] 3 1 A = Which answer is correct for the A ?

A: GivenA=3121

Q: If the determinant of a 4 x 4 matrix A is det(A) = -6, and the matrix C is obtained from A by…

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Q: 2. Find the general matrix output in terms of a, b, c, and d of T(ar³ + bx² + cx + d) when –12 12]…

A: in the given question we have to find the genral matrix output in terms of a,b,c,d for this first…

Q: and Y = (1 1 -) If X =0 1. Find the matrix Z where Y = Xiz %3D -2

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Q: Find the matrix M of the linear transformation T : R² → R² given by -8x1 + 9x2 5x1 – x2 x1 X2 M =

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Q: Solve for the value of x from the given matrix: [(x-2) y (2z - j)] = [(y+z) j2 (x-1)]

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Q: A is a 3 x 3 matrix with det(A) = -2. What is the determinant of A-1 AT? Here AT is the transpose of…

A: Given; AT = A So, A-1AT = A-1A = Identity Matrix

Q: Suppose that a 4 x 4 matrix A with rows v1, v2, v3, and v4 has determinant det A = 2. Find the…

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Q: (b) Find the Jacobian matrix ду əx where y [1+1+2+3 -x1x2x3 -[1+5+ = -B X2 I3 and x =

A: (b) Given y=1+x1+x2+x3-x1 x2 x3 and x=x1x2x3   To Find: The Jacobian Matrix ∂y∂x

Q: Q1. Find determinant of the matrix 4 -1] а) 2 2 2 0 -1 4] -1 2 b) 3 3 0 1 2 2 3 1 -1 1 -1 1 -1 1 c)…

A: According to guidelines, we solve only first 3 parts, thank you.

Q: Find the de terminant OF the matrix below : * [: ] 3 d. 2 a. -2 4 -5 4 2 b. 3s - 2 Cos -1 e. 3 1-t…

A: The given matrices are: a. 31-24 b. 13s-126s-1 c. 13t26t d. 102-541121 e. 331-t4-t

Q: find the determinant of the nxn matrixx A with 3's an the diagonal, 1's above the diagonal, and O's…

A: Given: The matrix A is n×n. Also, 3's is on the diagonal of the matrix. 1's above the diagonal of…

Q: Find the determinant of the n X n matrix A with 3's on the diagonal, 1's above the diagonal, and 0's…

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Q: Let A be a symmetric 2 X 2 matrix and let k be a scalar. Prove that the graph of the quadratic…

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Q: 2. Write the quadratic function f(x,,y;)=-3x; +2x,x, – 3x; – 4x, – 4x, +6 in matrix form as f(x) =…

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Q: Solve the equation SP = S to find the stationary matrix S and the limiting matrix ¯¯¯P.

A: P is a regular matrix so there must exist a stationary matrix S such that SP=S  Where, S=a bc The…

Q: If the determinant of a 4×4 matrix A is det(A)=2, and the matrix D is obtained from A by adding 5…

A: Given det A= 2  D can be obtained by adding 5 times the third row to the second in A  See the…