Define a linear transformation g : R3 R3. The matrix representation of g over standard bases is given by 3 -1 G= 7 5 1 7

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Define A Linear Transformation G R3 R3 The Matrix Representation Of G Over Standard Bases Is Given By 3 1 G 7 5 1 7 1 (21.78 KiB) Viewed 25 times

Define a linear transformation g : R3 R3. The matrix representation of g over standard bases is given by 3 -1 G= 7 5 1 7 2 0 -4 .. a (a) 3 points) Write out the formula of g, i.e., find out the expression of go). (9) (b) [8 points) Determine the column space and null space of matrix H (i.e. Col(H) and Nul(H)) and the dimensions of Col(H) and Nul(H), respectively. (c) 19 points] Given vectors u1, 12, 13 € R. It is known that g(u: +2u9 +313) = 2 9 -4 g(4u1 + 8u3 + Oug) = 12 ..) -16 Find out all possible u3 satisfying the above two equations.