Find a fundamental matrix of the following system, and then apply x(t) = Þ(t)Þ(0)¯ ¹x₁ to find a solution satisfying the initial conditions. 1 || 2 5 -6 0 x' = 4 - 1 - 4 x, x(0)= 0 8 -2-8 Find a solution satisfying the given initial condition. x(t) = (Use integers or fractions for any numbers in the expression.)

Q: 2 et A be an invertible matrix such that A-¹ = 0 -1 2 01 1 1. Solve the system (4A²)x= b, where b =…

A: Given:To Solve: , where .

Q: Some of the entries of the 3 x 3 matrix A are known as A -1 1 If det (A) = -–6 and A-1 find x.

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Q: Convert the augmented matrix [5 -3 4 2 || || -3 0 -5 to the equivalent linear system. Use x1, x2,…

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Q: For each of the following, factor the matrix A into a product QDQT where is orthogonal and D is…

A:

Q: 11.) Solve using matrices and Gaussian elimination: x + y + z = -3 -x + 3y + 2z = -8 2x + z = -3

A: Given: x+y+z=-3 -x+3y+2z=-8 2x+z=-3

Q: The characteristic polynomial of the matrix A: · PA (A) = x² - 15+8 · PA (λ) = x² - 81+13 ·PA (λ) =…

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Q: Form a coefficient matrix for the following linear system of equations: √x + 16 y = 11 x + 2y = -1.…

A: Given that The system of equations are x+16y=11x+2y=-1 compare to Ax=b

Q: Matrix A is order 5 x 5 and matrix B is order 5 x 5. Find the order of AB and BA, if they exist. (If…

A: Two matrices A and B are said to be conformable for the product AB if the number of columns of A be…

Q: (1) Show that I + Y X is also invertible. (2) Show that Y (I + XY )−1 = (I + Y X)−1Y .

A: This is the problem of Linear Algebra, Linear Transformation. Given: X is a m×nmatrix and Yis a n×m…

Q: 6) Let I denote the 2 x 2 identity matrix. (i) Given the equation: (1+24¹) 1 12 26 T (ii) Given the…

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Q: 4 -4] find A3. 0 -5 Given the matrix A = A³ =

A: Given: A=4-40-5

Q: Given the matrix 2 1 A = |0 3 1 1 0 -1 and the polynomial p(x) = x³ + a.x² + bx + c, find the values…

A: GivenA=21003110-1p(x)=x3+ax2+bx+cp(A)=Op(A)=A3+aA2+bA+c=O21003110-1.21003110-1.21003110-1+a21003110-…