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Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 1: Q3E (page 5)

in exercises 1 through 10, find all solutions of the linear systems using elimination.Then check your solutions.
3. $|2 x + 4 y = 3 3 x + 6 y = 2|$

Short Answer

Expert verified

The given system of equations has no solution.

Step by step solution

01

Step 1:Transforming the system

To get the solution, we will transform the value of x,y

$| 2 x + 4 y = 3 3 x + 6 y = 2 |$ Into the form $|x = . . . . y = . . . .|$

02

Eliminating the variables

In the given system of equations, we can eliminate the variables by adding or subtracting the equations.

In this system, we can eliminate the variable x from equation 1. First of all multiply the first equation by 3 and multiply the second equation by 2.

$|6 x + 12 y = 9 6 x + 12 y = 4|$

Now subtract the second equation from the first equation.

$|6 x - 6 x + 12 y - 12 y = 9 - 4 6 x + 12 y = 4| = |0 = 5 6 x + 12 y = 4|$

Now we can for the any value of x,y the 0 will never be equal to 5.

Hence, the given system of equation has no solution.

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Most popular questions from this chapter

In exercises 1 through 10, find all solutions of the linear systems using elimination. Then check your solutions

7. $|x + 2 y + 3 z = 1 x + 3 y + 4 z = 3 x + 4 y + 5 z = 4|$

Question: Give a geometrical description of the set of all vectors $\overset{鈬赌}{u} i n R^{2}$ such that $\overset{鈬赌}{u} . \overset{鈬赌}{v} = \overset{鈬赌}{u} . \overset{鈬赌}{w}$ .

Find the function $f (t)$ of the form $f (t) = a e^{3 t} + b e^{2 t}$ such that $f (0) = 1$ and $f' (0) = 4$ .

Balancing a chemical reaction. Consider the chemical reaction

$a {NO}_{2} + b H_{2} O 鈫� c {HNO}_{2} + d {HNO}_{3}$ ,

where a, b, c, and d are unknown positive integers. The reaction must be balanced; that is, the number of atoms of each element must be the same before and after the reaction. For example, because the number of oxygen atoms must remain the same,

$2 a + b = 2 c + 3 d$ .

While there are many possible values for $a, b, c$ and d that balance the reaction, it is customary to use the smallest possible positive integers. Balance this reaction.

Compute the products $A \overset{鈫�}{x}$ in Exercises 16 through 19 using paper and pencil (if the products are defined).

19. $[\begin{matrix} 1 & 1 & 鈭� 1 \\ 鈭� 5 & 1 & 1 \\ 1 & 鈭� 5 & 3 \end{matrix}] [\begin{matrix} 1 \\ 2 \\ 3 \end{matrix}]$

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