Let T : P3 → R³ be defined by 2а — 2b + с — Зd -a + 36 + 2c – 3d . Let u = x – 3x. B = {1,x, x² , x³ }. and За — Зс — 2d T (ax³ + bæ² + c + d) %3D | 0. C = -3 0 . use the Fundamental Theorem of Matrix Representations to find 2 -2 1 Given [T -3 5 1 4 -3 -5 1 Pc(T(u)). Ex: 5 Pc(T(u)) =

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A:

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A: According to the question,

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A: To get the matrix A for a rotation about the z-axis through an angle of pi/2 counterclockwise, we…

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A: For the solution of the problem follow the next step.

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A: Given matrix is A=1001-1-1

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Q: .

A: A=02-123-2-1-20 To find: An orthogonal matrix U that diagonalizes .

Q: Let A = (a) and B = (A + B)(A + B) (b) A2 + 2AB + B² 3) Let A2 and B2 denote the matrix products AA…

A: A=5423B=8759

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Q: Let A be an nxn matrix. Prove that dim(col(A²)) < dim(col(A)).

A: Given: Assume that, A is an n×n matrix.

Q: 6 -1 Evaluate ABT – 3C given that (2 -2 lo -1 2. -2 A = 6 -3 ‚B = and C = -12 7. 3. Use matrix…

A: To solve the given matrix problems.

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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A: The detailed solution is given below Thank you

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A: Here, CA=I, where I is the identity matrix.

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Q: Statement: "Let A and B be n x n matrices, where the columns of A span IR" and B is not equal to the…

A: The given statement is false.

Q: Let T: R² → R² be defined by T = {[5].[a]} C= Given Pc 1 -2 = [223] -2 5 [T](PB (u)) = Ex: 5 ([2/2])…

A:

Q: IK, ar U₁ = 2 vecte U2 = U1, U2, U3 3a + 3 2a +3 a²+3a 7 113 = 4a - 2 3а-1 2a² a) Show that the rank…

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A: The given transformation in vector form is  Tx1x2x3x4=7xx+2x2-x3+x4x2+x3-x1

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A: An upper triangular matrix is a triangular matrix with all elements equal to below the main…