4) Consider the function from T: R³ → R² given by X T: y = x + 2y - Z x+z Z (i) Show that T'has the additivity property. (ii) Show that T'has the homogeneity property. (iii) Find the standard matrix for T. [Hint: Let u = X y р and v= 9 when showing additivity and let k be a Z general scalar when showing homogeneity.]

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A: T1: R2 → R2, T1(x, y) = (x − 5y, 5x + 4y) T2: R2 → R2, T2(x, y) = (y, 0) Now T = T2 o T1 (x,y) = T2…

Q: Find T(v) by using the standard matrix and the matrix relative to B and B'. T: R² R², T(x, y) = (2y,…

A: Introduction: To find the standard matrix related to any basis first find the images of the basis…

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