Find the matrices associated with the following linear maps:

(a) F:R4→R2F : \mathbb{R^4} \rightarrow \mathbb{R^2} defined by F((x1,x2,x3,x4)t)=(x1,x2)tF((x_1, x_2, x_3, x_4)^t) = (x_1, x_2)^t

(b) F:R4→R4F:\mathbb{R^4}\rightarrow \mathbb{R^4} defined by F((x1,x2,x3,x4)t)=(x1,x2,0,0)tF((x_1, x_2, x_3, x_4)^t) = (x_1, x_2, 0, 0)^t

(c) F:Rn→RndefinedbyF : \mathbb{R^n} \rightarrow \mathbb{R^n} defined by F(X) = -X$

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1 Answer

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Hint:

Try substituting the standard unit vector into the function FF.

The matrices can be expressed as [F(e1)…F(en)]\begin{bmatrix} F(e_1) & \ldots & F(e_n) \end{bmatrix}