Write the following system in matrix notation 1 i1(t) = –tx3(t) + t°r«(t) – 2tx2(t) + t +1 i2(t) = –x3(t) – 3x1(t) + cos²(t) i3(t) = –9x2(t) + (tan t)x1(t) + 3t sin (t)x4(t) ¢4(t) = –x4(t) + (tan (t))æ1(t) + 6.

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A: Given: R3×3=cos θ-12sin θ12sin θ12sin θ12+12cos θ12-12cos θ-12sin θ12-12cos θ12+12cos θ To find:…

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Q: rewrite ax^2+by^2+cz^2+dxy+exz+fyz+gx+hy+iz+j=0 in  standard form by matrix

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Q: (b) B={(-1,3), (2, -1)} and 8' = {(0, 10), (5,0)} (c) B={(2,5), (-1, -3)} and 3' = {e1, e2} (d)…

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Q: dz (b) Determine the by using the Chain rule with the following information: ds z = cos (rªy^) – sin…

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Q: Given matrix A = [ 4 3 3                                 3 4 3                                 3 3…

A: Given matrix is, A=433343334 The objective is to find the determinant A290+I-1 Now, the determinant…

Q: For matrix A and a scalar k, (kA)T is equal to: k(A^T) k(A) (k^2) x (A) (k^2) x (A^T)

A: We will solve the matrix operation.

Q: 2. A = 77₁b = 3 25 -1 3

A: Given, .If A=, than .

Q: Suppose A is a non-singular matrix. Using properties of the determinant, show that det(A^−1) =…

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Q: 1 6. Let A = 5 [; ] [:] 3 and B = 1 0 2 (a) Calculate the matrix Aª. (b) Calculate the matrix B-2.…

A: Use the properties of matrix and matrix multiplication to determine the value of each term. The…

Q: Write a'= -3x+y+ln(t), y'= t'a in matrix form as 18 31 and f(t) is 181 [*] -= P(1) [*] + f(t) where…

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Q: 4. y= cje²*+c2xe²*

A: Please see the below picture for detailed solution.

Q: (4) Given a matrix X of independent variables, psudo-inverse X† is defined as (X"X)-'x" (a) If X is…

A: If a matrix is of order (mXn) then transpose of A is of order (nXm).

Q: 1 2 3 1[1 1 07 M = 20 0 1 3|1 0 0

A: Write the relation M as a set of ordered pairs. If x,y is an ordered pair in M , then (y,x) is and…

Q: A' is a 1X3 matrix. The least square solution to the equation A'x=28 is the vector x* =[1 2 3]'…

A: Given that, A' is a 1×3 matrix. A'x=28 ,x*=1 2 3'

Q: Let -5 ^-[33] ²-[+ ₂] = [42], A = E = =-[B] F-[-2] -1 Compute the indicated matrix. (If this is not…

A: We are given three matrices A,E and F. We have to find E(AF)=?

Q: cos no sin ne - sin no cos no 4 -1 5 -4 -2 1 -3 1 -5 2 2 -1 3.

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Q: +00 1 Σ n=3 n · . Inn - +00 Σ m=1 3η5 + cos2 n – 1 4m? – 15 + π

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Q: find linear systems (matrix) x'(t) =[ 11 - 15 6 - 7 ] x(t) classify its origin

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Q: If the matrix of change of basis form the basis B to the basis B' is A = OA. 2 (²₂) OB.-2 OC (-2) 3…

A: Given that the matrix of change of basis B to the basis B' is A=-32-21, then find the second column…

Q: (a) Consider the system of equations 11х3 — Зх1 yi %3D - 7x1 – 6x2 – 5x3 y2 х> + 2х3 — 2х = y3…

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Q: if the chractrestic polynomial of a matrix A is p(^) = (^ +1)(^ - 2)2 then det(-A) +tr (A) = 1 7 -2…

A: As we have 3 roots of characteristics polynomial.

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Q: Let A and B be 4x4 matrices such that det(A) = 5 and det(B) = 3. Compute the determinant of…

A: Explanation of the answer is as follows

Q: 2 A= 2 4 3 一 1 -2 1 (i) Find A by using cofactor method. (ii1) Find (4) by using adjoint matrix. 19

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Q: 1 (2¹) 4 4

A: Given matrix as, A=-2144

Q: Evaluate the determinant using Chio's method.

A: We have to find the determinant of the given matrix by chio's  method.

Q: Let T: R³ → R² be defined by T -~--~--E) ----B]}~~(~-| ||-~ ~[]) Let B = u₁ U3 = { = [3], , = 6 (ED)…

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Q: Use determinant to find the equation of the line that passes through the points (4, ― 3) & ( ―1,2)

A: We have to find equation of line using given information Concept required: Equation of line passing…

Q: 5. y= e²^(c,cosx+c,sinx)

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Q: Using the equation for the time derivative of a DC matrix C, W2 -W3 Ċ + S(@)C = 0 where S(@) = | w3…

A: We are given the following equation.   C˙+S(ω⇀)C=0 where S(ω⇀)=0-ω3ω2 ω30-ω1 -ω2ω10 Let us denote…

Q: If the matrix A= [2 5 1;7 3 6;2 5 4], find: A' A(2,3) size(A) LA(:,2)=[] Inv(A)

A: We can solve this as follows:

Q: 2. Find fundamental (3 (a) x' = (b) x' = 2-5 4 matrices for the following systems: :)> (9) -2 62 5 3…

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Q: Assuming that all matrices aren X n and invertible, solve for D. CAB" DAC"B = CA". OD =…

A: I am attaching image so that you understand each and every step. Given:- All matrices are n x n and…

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Q: For a non-singular matrix A, A^(-1) is equal to: (adj(A)) / det(A) det(A) x (adj(A)) det(A) x A

A: Explained below