2. You have some coins, each of which is a penny (1 cent), a nickel (5 cents), a dime (10 cents), a quarter (25 cents), or a half-dollar (50 cents). You know that • you have three times as many dimes as quarters, the number of pennies and nickels combined is one more than the number of dimes and quarters combined, you have 13 coins in total, and the total value of your coins is $2.68 (268 cents). (a) Set up (do not solve) a system of linear equations for the numbers of pennies (p), nickels (n), dimes (d), quarters (q), and half-dollars (h) you have. (b) Write down the augmented matrix corresponding to your linear system from part (a). (c) Is it possible that there a unique solution (where p, n, d, q, and h are real numbers) to your linear system from part (a)? Answer yes or no (no justification necessary).

2. You have some coins, each of which is a penny (1 cent), a nickel (5 cents), a dime (10 cents), a quarter (25 cents), or a half-dollar (50 cents). You know that • you have three times as many dimes as quarters, the number of pennies and nickels combined is one more than the number of dimes and quarters combined, you have 13 coins in total, and the total value of your coins is $2.68 (268 cents). (a) Set up (do not solve) a system of linear equations for the numbers of pennies (p), nickels (n), dimes (d), quarters (q), and half-dollars (h) you have. (b) Write down the augmented matrix corresponding to your linear system from part (a). (c) Is it possible that there a unique solution (where p, n, d, q, and h are real numbers) to your linear system from part (a)? Answer yes or no (no justification necessary).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 27EQ

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