Define A Linear Transformation G R3 R The Matrix Representation Of G Over Standard Bases I E Standard Matrix Is 1 (100.21 KiB) Viewed 36 times
Define a linear transformation g :R3 +R$. The matrix representation of g over standard bases (i.e., standard matrix) is given by 3 -1 G= 7 5 0 7 2 1 -4 a (a) (3 points) Write out the formula of g, i.e., find out the expression of g( b ( . с (b) (8 points) Determine the column space and null space of matrix G, and find the dimensions of Col(G) and Nul(G), respectively. (c) (9 points) Given vectors u1, U2, U3 € R3. It is known that 2 9 g(u+ 2u2 + 3u3) ..) -4 g(4u1 + 8u2 + Ouz) = 12 -16 Find out all possible uz satisfying the above two equations.
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. с (b) (8 points) Determine the column space and null space of matrix G, and find the dimensions of Col(G) and Nul(G), respectively. (c) (9 points) Given vectors u1, U2, U3 € R3. It is known that 2 9 g(u+ 2u2 + 3u3) ..) -4 g(4u1 + 8u2 + Ouz) = 12 -16 Find out all possible uz satisfying the above two equations.