Find the standard matrix, A, for the following transformation E-H = x+y+z 2x-y+z ] 3 T: R³-R² given by (i) What is the rank of A? Justify your answer (ii) What is the nullity of A? Justify your answer

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: Let A and B be matrices of the form: b, b, b 12 13 ba bz ba b, bz ba A= B= 43 a b4 b. ba Consider…

A: Yes, This is a linear Transformation from R6 -> R9 .

Q: The linear transformation 2x y T 3z+w X - w is written as a matrix multiplication T : A What is the…

A: The linear transformation,Txyzw=2x3z+wx-w

Q: Characterize the image and kernel of the following matrices: 1 (443) -2 2 2

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Q: 2. Diagonalize each matrix, if possible. Give the similarity transformation. 7 4 (a) -6 (b) [ (c) 4…

A: Given A, we have to find M such that M-1AM is diagonal A=74-6-3 ∴A-λI=0⇒7-λ4-6-λ-3=0⇒λ-3λ-1=0⇒λ=3,1…

Q: Consider the following (real, symmetric) matrix: A-(10 40 = 40 158 Determine the real canonical form…

A: Given:  A=104040158 To find the real canonical form of a given matrix.

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

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: Can you find the A (matrix) for the following? Can you use the transpose properties, such as taking…

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Q: Find the B-matrix for the transformation x-Ax when B=(b₁,b₂, b3}. A= -7 -72 1 17 -4 -72-21 The…

A: Solution :-

Q: Find the matrix A of the linear transformation from R² to R³ given by T([2]) = 4-88 A = 91 +5

A: Given:- Tx1x2=693x1+-75-6x2

Q: Find a matrix A that induces the transformation T:R3R given below. |-8x-2y-2z -5x+6y+6z T

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