Find the matrix exponential of -3x1 + 8x2 x2 = 12x1 – 7x2 and use the matrix exponential to solve the IVP X1(0) 1 X2(0) -1

Q: Use the inverse matrix method to solve Ax = b below X = (x, +2x, = 3 (2x, – x, = 1

A: Given that  To solve the given system by using inverse matrix method. X1+2x2=3 2x1-x2=1

Q: Express f in matrix notation where f(ū, 7) = 3x1Y1 – 2x2Y2 + 7x2Y2 – 8x2y3 + 4x3Y2 6x3Y3

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Q: Solve the following equations 2x + 3y = 7 ,4x –- 2y = 6 by using: 1- Cramer's Rule 2- Inverse matrix…

A: Answer(1):

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

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Q: Solve the matrix by using Gauss elimination method x +2z35 3x+4y+2z%3D8 X+3z-10

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Q: By using the matrix fundamentals, solve the set of linear equations of: 2x1 + 3x2 - 5x3 = 1 X1 + x2…

A: First write the equation in matrix form AX=B then find determinant of A.. Then fd inverse of A…

Q: Solve by Matrices method

A: Given system of equation is 2x1−x2+x3=8x1+2x2+x3=6x1−2x2−x3=1........1 Now write the the system (1)…

Q: Find the symmetric matrix A associated with the given quadratic form.             5x12 -x22 + 2x32 +…

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Q: solve by finding an inverse matrix 2x+y=6 x+2y+z=12 x-y-z=-5

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Q: Solve for the matrix X eMz (R): -2 3 ļ s X = 7|o

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Q: Find a matrix X that solves the equation 1 2 3 4

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Q: Solve by the fundamental matrix method, 3 r2(1)

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Q: Compute the matrix exponential e for the following system x' = Ax. x'1 = 10x, - 14x2, x'2 = 2x, - X2…

A: First we will obtain the metrics A from the given system of differential equation then we will…

Q: How matrix notation helps in simplification of computations with systems of differential equations?

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Q: Find x such that the matrix is equal to its own inverse. 7 x A- -4 -7 X =

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Q: Find the inverse of the elementary matrix.

A: Now,

Q: Matrix A is 2 x 7 and matrix B is 2

A: Given, Matrix A is 2 x 7 and matrix B is 2 x 8.

Q: 11. If a and B are the roots of the quadratic 3.x2 - 4x +6 = 0, find the value of (+) -3 12. For…

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Q: Write the 4 x 4 elementary matrix which accomplishes the row operation R3 - 5 R2 ---> R3 when you…

A: let  I be the 4×4  identity matrix I=1000010000100001

Q: : Find the inverse of the matrix 1 1 -1 0 -2 1 A = 3 -1 2 with using the method of Cofactor…

A: firstly find cofactor of A and then adjoint and use  A-1 = adjA/|A|

Q: Find a formula for the quadratic form that does not use matrices. 2 -5 [ * y ] -5 7 -5 [ x y -5 7

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Q: Find the matrix of the quadratic form associated with the equation. 12x2 - 4xy + 26y² - 56 = 0 I3D

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Q: How can you solve this matrix with the equation? (AT + 4I ) −1  =    −2 5 1 4

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Q: Solve the matrix equation Ax = 0, where

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Q: Use the definition of the matrix exponential to

A: Given,           X'(t)=01-10X(t)

Q: Solve for the matrix X: 35 and X12 The first row of X is given by is X11 = and X22 and the second…

A: X11=-2 X12=1 X21=3 X22=-1

Q: Find the inverse of the matrix if it exists.

A: Given: The matrix A=200040006. Inverse of the matrix A is given as, A-1=1AadjA

Q: Solve for the 2 x 2 matrix X: X + 2 23 5 3 X.

A: Introduction: A-1 stands for Inverse of Matrix for matrix A. There is a straightforward formula for…

Q: Solve for x and y in the matrix equation below: [10 3 2 6x -9 3 -4 4על 2. 4 3 [1 2-1 x -8 -3 3x 0

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Q: [1 2) 13 · X = 2-

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Q: Solve by matrix inversion:…

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Q: Find the inverse of the matrix (if it exists).

A: Now determinant A is,

Q: Find the inverse matrix of [2 1 -1

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Q: Solve the matrix equation for x -2 1 4 3 2 1 -1 -1| X = 6. 7 8. 9. 1 1 -4 1 3 7 9.

A: The solution is given in the next steps.

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

A: The given matrix is, A=30-350730-3. Obtain the Eigen values of the given matrix.…

Q: Find the inverse of the matrix. 5 4 -3 -2

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Q: 5. Use the inverse of the matrix [32¹] to solve the system 3x1 x2 = 9 3x1₁+ 2x2=1

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Q: G (190)-(-) Solve 1 using the inverse of a matrix.

A: The given equation is 1-1-111-1110xyz=9-116 find the inverse of matrix 1-1-111-1110100010001 operate…

Q: Solve the matrix equation AX = B for X. 3 1 2 B = 7 A = 4 2 3 10 X3D

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Q: 3 - 3 1 /- 1

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Q: Solve the matrix equation Ax = 0.

A: Given:

Q: Find the hessian matrix for y = x12 + 2x22

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Q: Use matrices to solve x + 2y = 1 3x + 2y + 4z = 7 −2x + y − 2z = − 1

A: Given that x + 2y = 13x + 2y + 4z = 7−2x + y − 2z = − 1

Q: Solve using an augmented matrix. 2x1 + x2 = 4.x1 – x2 = -7 1

A: The given system of equation is -  2x1 + x2 = 14x1 - x2 = -7 We will first change the given system…

Q: Explain how to solve the matrix equation AX = B.

A: We have to explain how to solve the matrix equation: AX=B Assuming system of linear equations with…

Q: Matrix A is 2 x 7 and matrix B is 2 x 8. BTA is dimension

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Q: Solve the matrix equation for X: 1 1 1 -1 -1 1 3 X 1 -6 1 9 3 i

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Q: State the quadratic form of a general multivariate function in three variables and give the matrix…

A: A quadratic function f : R→R has the formf(x)=a.x2Generalization of this notion to three variablesis…

Q: Solve the matrix equation for X: - 1 1 1 4 1 -3 3 1 1-1

A: A-1A =I =AA-1 , where , A is an square matrix. A-1 = 1A adjA