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5. Let LR2 R3 be the mapping defined by L(x1, x2)=(x1+ 2x2, 2x1 + 4x2, x1). (a) Prove that L is a linear mapping.

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5. Let LR2 R3 be the mapping defined by L(x1, x2)=(x1+ 2x2, 2x1 + 4x2, x1). (a) Prove that L is a linear mapping. (b) Find the standard matrix of L. (c) Find a basis for the range of L. (d) Find a basis for the kernel of L.

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