Use projection matrices to find the matrix exponential and particular solution of the given linear system x' = Ax + f(t), x(a) = x. 4 x' = - 16 x, f(t) = 1612 x(0) = - 4 4t ..... Find the projection matrix(matrices) for A. 1 0 The projection matrix(matrices) is/are 0 1 (Type exact answers, using radicals and i as needed. Use a comma to separate matrices as needed.) Find the matrix exponential. 1+ 4t - 16t e At t 1-4t

Q: Find the matrix of the quadratic form 2x,² + 3x2² – x3² – 4x1x2 +2 x1X3 + 6x2X3

A: The symmetric matrix for quadratic form ax12+bx22+cx32+dx1x2+ex2x3+fx1x3 can be written as…

Q: Let's consider the following system of equations: F₁ = x² + x² − 2 = 0 F₂ = x²₁x²₂ - 1 = 0 0 Solve…

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Q: Let D = Find A6. A6 [1 2] and P = C 1 – 3 0 9] and consider the matrix A = PDP-1

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Q: -1 -1 | | 4. For the semidefinite matrix A = -1 2 -1 write x' Ax as a -1 -1 sum of two squares.

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Q: Stein equation. A Stein equation with respect to square matrix X has the form AXB-X+Q = 0, where A.…

A: note :  Since you have posted multiple questions with multiple sub parts, we will provide the…

Q: 9. A = -2 2

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Q: Jse Use the following set of equations to solve questions (7,8, :9, 10, 11, 12) based on Gauss…

A: Given : 2x1+x2-x3=23x1-2x2+x3=1x1-2x2+2x3=-1` The above system of equations can be written in matrix…

Q: Find the characteristics equation of the matrix [1 2 A -2 -1 01 and hence find A-.

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Q: (v) 0 -1 0 1 0 0 ma ~ 0 ( 1 a -1 0 0 0 a 0 0 a 1 0 1 000

A: Given: A matrix .To find: The Row operations by which the matrix is reduced to

Q: Consider the LP problem: Maximize 3xı + 2x2 subject to: x1 – x2 + 2x3 9 3x1 + x2 – x3 0 Find the…

A: Given LP problem is, x1-x2+2x3≤82x1+x2-x3≥6x1+3x2≥93x1+x2-x3≤10x1,x2,x3≥0 The canonical form of LP…

Q: 4. Determine if the following sets are linearly independent or linearly dependent. Justify your…

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Q: * Find the Matrix B from order 2 x 4 , Its elements are written in the form by = i + ()

A: Here we find matrix B of order 2×4

Q: Let matrix A = 1 1 1 3 2 1 −2 3 1 (a)Find two distinct row echelon forms of A. (b) Find the…

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Q: -2 Find C, where matrix C = [3/2 -1/2

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Q: 5) Find dx/dt of Matrix: X 5e-1 2e-¹ -7e-t

A: We know , d/dx(e-t) = -e-t   Given X = 5e-t2e-t-7e-t

Q: -*₁+3x₂ = 2 2x1 + x2 + 4x3 = 3 x₂ + 2x3 = 4 (a) Using [IA]~ [A¹1], Find A-¹. (b) Find Adj A.…

A: note : Since you have posted multiple questions with multiple sub parts, we will provide the…

Q: Given F(x) = 4₁ 21 -2x1 3 4x2 3 2x1²x24 2x15x2 calculate the matrix Jp ([^])

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Q: Solve the matrix by using Cramer's Rule method 2x+5y+2z=10 3x+8y+z=3 2y+5z=1

A: To solve the matrix by using cramers rule method.

Q: For R1: y=2x2-3x-5, R2: y=x2-x-2,

A: answer is in next step

Q: Find two linearly independent solutions of y" +9ay=0 of the form 3₁=1+a3a³+a6z6+... y2 = x+b₁x+b7x7…

A: The given differential equation .We have to find the solution of the differential equation using the…

Q: 5. Consider the matrix -1 3 0 0 1 0 3 A = 1 2 (a) Find A-1, the inverse matrix of A by using your…

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Q: X1+ X2 + 2X3 — 5Х4 %3D 3 - 2X1 + 5X2 – X3 – 9X4 = -3 2X1+ X2 — Хз — 3Х4 %3D —11 X1 – 3X2 + 2X3 + 7X4…

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Q: -) Use the inverse of the coefficient matrix to solve the system: x₁ + 2x₂ + 2x3 = 2 x₁ + x₂ + x3 =…

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Q: 2. Express the system of linear equations as a matrix equation in the form Ax =b. - .x1+ 2x2 + x3-…

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