4. Let V be a vector space over R with subspaces U and W. (e) Show that 1 0 -1 1 and define LA: R4 → R³ by (c) Let A = -[₁ 1 0 1 -1 1 1 x1 21 X2 LA: → A. TA TA Find the kernel of LÃ. Find a basis for the image of La. (d) Define a linear transformation L : R³ → R² by x1 x1 x2 L: X2 x2x3, x3, Find the kernel of L, the image of L, and calculate the matrix associated to L with respect to the standard bases of R³ and R². X2 x3 x3

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A: Please see the below picture for detailed solution.