Find the standard matrix of the composition T = T, o Tị for T1 (x, y) = (-x + 2y, x + y, x – y) T2 (æ, y, z) = (x – 3y, z + 3æ)

Q: 1. Calculate exp(A) where A is the 2×2 matrix given by A 7 -2 -[33] = 5 5

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

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Q: 3. Let 1 B -1 Consider T : R²,2 → R²2 defined by T(A) = AB – BA. Let - 이 [0 [o o] [o o] [1 0] Bị and…

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Q: Let A 2x2 matrix. A satisfies with tr (A² ) = 5 and tr ( A) = 3. Find determinant of A.

A: Use property of eigen value

Q: Express the linear function as F(x) = CX for some matrix C. f(x1,x2,x3,x4) = (5x3 - x1, 2x3 + x4,…

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Q: 1. Let B = {(1,3), (–2, –2)} and B' = {(-12,0), (-4, 4)} be bases for R2, and let A = be the matrix…

A: Matrix is a set of array in which elements are arranged in row and columns. For a matrix and ,…

Q: Find a matrix that implements the linear transformation T(x1,x2) = (3x1-4X2, X1-X2, 2x1 + x2)

A: A linear transformation is a function satisfying the following properties: where x and y are…

Q: Matrix obtained by changing the rows into columns or columns into rows is called O a. determinant O…

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Q: Illustrate the multiplying any row (or column) by a scalar do to the determinant?

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Q: Q6. Consider the function f: R³ R² defined by f((x, y, z))= (-2r, y + 32). (a) Show directly that f…

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Q: Find the matrix P that transforms S₁ to S₂ for the following pairs of bases. 1. S₁ = {(2, 5), (1,…

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Q: Let y = 1 2 and u= 4 2 Write y as the sum of a vector in Span (u) and a vector orthogonal to u.…

A: Introduction: The projection of a vector onto another vector is the application of dot product. This…

Q: [121] In other words, write A = SDS-¹ = SDSt where D is a diagonal matrix and S is an isome- try.…

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Q: Suppose V₁, V₂ € R³ are nonzero column vectors and V3 = 2v₁ - 32. What is the determinant of the…

A: Given: Suppose  are nonzero column vectors and  We have to find what is the determinant of the…

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: n 2. Check whether the matrix A- 2 Check whether the matrix A (0 is Hestnitian and Unitary matrix or…

A: The detailed solution is given below Thank you

Q: 2. Write the following functions in matrix form: (a) f(x1,x2, X3) = (x1 + 2x3, x1 + 3.x2 – x3, x1)…

A: Given the function is a fx1,x2,x3=x1+2x3, x1+3x2-x3, x1 In a matrix form…

Q: Find the equation (in standard form) of a circle containing points by using the matrices method:…

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Q: Find the characteristic equation of the given matrix: 8. -D1 2 0. A = 8 -D1 6 -6 1 6 5 Select one: O…

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Q: For the matrixA=daig(-2,-1,2), put the following values in increasing order: det(A), rank(A),…

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Q: Find the coordinate matrix of w= 2-3x+x?+x vector relative to base B= {1, 1-x, (1-x)?, (1-x)³} in…

A: Given, w = 2 - 3x + x² + x³

Q: 0 -2 2 -1 B = 1 4 -1 3 4

A: We have to solve given problems:

Q: Find the standard matrix of the linear transformation. -y x + 4y бх — 2у

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Q: 2x + 3y + 3z = 2 4x – 3y – 6z = 2 10x – 6y + 3z = 0 The determinant of the matrix is

A: We need to find the determinant of coefficient matrix. We will use Cramer'r rule to solve the…

Q: Find the determinant of x from the given matrix: 4 -123 2021 10 301 14 2 4 5 -35 -30 -28 -25

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Q: Express the determant expression of a 3 X 3 matrix using cofactor and minor, Using this, try to…

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Q: Find the standard matrix for the linear transformation T. T(x, Y, z) = (x+ z, x - y, z -y)

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