1 answer

Please show work Consider the following linear transformation T: RS → R3 where T(X1, X2, X3,...

Question:

Consider the following linear transformation T: RS → R3 where T(X1, X2, X3, X4, Xs) = (x1-X3+X4, 2x1+x2-X3+2x4, -2x1+3x3-3x4+

Please show work

Consider the following linear transformation T: RS → R3 where T(X1, X2, X3, X4, Xs) = (x1-X3+X4, 2x1+x2-X3+2x4, -2x1+3x3-3x4+xs) (a) Determine the standard matrix representation A of T(x). (b) Find a basis for the kernel of T(x). (c) Find a basis for the range of T(x). (d) Is T(x) one-to-one? Is T(x) onto? Explain. (e) Is T(x) invertible? Explain

Answers

The matrix representation @T(1,0,0,0,0) = (1,2,-2)=1 (1046) 426010)-26.) +601110,0,0) T0100,0,1) is - 1,0) = 0 (1,0,0) +1 (0,the © In In R of the part 6, the Column space is 1st, 2nd, and columns of A So, basiy for the range of Tn) - } ملے ۔ 2 725 d

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