7. Let L : R R be defined by L(x, y, z) = (x-y, x+2y, z),...

 

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7. Let L : R R be defined by L(x, y, z) = (x-y, x+2y, z), then: (i) Show that L is a LT. (ii) Find a basis for kernel(L). (iii) Find a basis for range(L). (iv) Is L one-one? (v) Is L onto? (vi) Is L invertible? (vii) Find the matrix corresponding to the standard basis of R. 7. Let L : R R be defined by L(x, y, z) = (x-y, x+2y, z), then: (i) Show that L is a LT. (ii) Find a basis for kernel(L). (iii) Find a basis for range(L). (iv) Is L one-one? (v) Is L onto? (vi) Is L invertible? (vii) Find the matrix corresponding to the standard basis of R.