A=[1224] Recall that row(A) and nul(A) are orthogonal complements. So we can split any x∈R2 into a unique component xr

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: A 12 24 Recall That Row A And Nul A Are Orthogonal Complements So We Can Split Any X R2 Into A Unique Component Xr 1 (51.86 KiB) Viewed 33 times

A=[1224] Recall that row(A) and nul(A) are orthogonal complements. So we can split any x∈R2 into a unique component xr in row (A) and a unique component xn in nul(A) such that x=xr+xn. PART A) Give a basis for row (A) and nul(A) PART B) Find Prow (A) (the projection matrix onto row (A)) and Pnul (A) (the projection matrix onto nul(A) ). What is Prow(A)+Pnul(A) ? PART C) Let x=(0,3). Compute xr and xn using your answers from part b. PART D) Provide a sketch which displays row (A),nul(A), and the x1xr and xn from part c. PART E) || xr∥ measures the shortest distance from to . (Fill in the blanks so that the statement is true. No explanation needed.)

A=[12​24​] Recall that row(A) and nul(A) are orthogonal complements. So we can split any x∈R2 into a unique component xr

A=[12​24​] Recall that row(A) and nul(A) are orthogonal complements. So we can split any x∈R2 into a unique component xr

A=[1224] Recall that row(A) and nul(A) are orthogonal complements. So we can split any x∈R2 into a unique component xr

A=[1224] Recall that row(A) and nul(A) are orthogonal complements. So we can split any x∈R2 into a unique component xr