Let A = {4, 5, 7} and B = {x, y}. Let p1 and p2 be the projections of A ✕ B onto the first and second coordinates. That is, for each pair (a, b) A ✕ B, p1(a, b) = a and p2(a, b) = b.(a) Find p1(4, y) and p1(7, x).What is the range of p1? (Enter your answer in set-roster notation.)(b) Find p2(4, y) and p2(7, x).What is the range of p2? (Enter your answer in set-roster notation.) Let A = {4, 5, 7} and B = {x, y}. Let p, and p, be the projections of A x B onto the first and second coordinates. That is, for each pair (a, b) E Ax B, p,(a, b)and p,(a, b) = b.= a(a) Find p,(4, y) and p,(7, x).P1(4, y)P1(7, x) =What is the range of p,? (Enter your answer in set-roster notation.)(b) Find p,(4, y) and p,(7, x).P2(4, y)=P2(7, x)What is the range of p,? (Enter your answer in set-roster notation.)

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Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.6: The Matrix Of A Linear Transformation

Problem 1AEXP

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Let A = {4, 5, 7} and B = {x, y}. Let p₁ and p₂ be the projections of A ✕ B onto the first and second coordinates. That is, for each pair (a, b) A ✕ B, p₁(a, b) = a and p₂(a, b) = b.

(a) Find p₁(4, y) and p₁(7, x).

What is the range of p₁? (Enter your answer in set-roster notation.)

(b) Find p₂(4, y) and p₂(7, x).

What is the range of p₂? (Enter your answer in set-roster notation.)

Let A = {4, 5, 7} and B = {x, y}. Let p, and p, be the projections of A x B onto the first and second coordinates. That is, for each pair (a, b) E Ax B, p,(a, b)
and p,(a, b) = b.
= a
(a) Find p,(4, y) and p,(7, x).
P1(4, y)
P1(7, x) =
What is the range of p,? (Enter your answer in set-roster notation.)
(b) Find p,(4, y) and p,(7, x).
P2(4, y)
=
P2(7, x)
What is the range of p,? (Enter your answer in set-roster notation.)

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