Explanation Given information: Consider the following equations: a + 6 b + 3 c = − 14 2 a + b − 2 c = − 8 − 3 a + 2 b + c = − 8 Calculation: Solve the equation a + 6 b + 3 c = − 14 for a as follows: a + 6 b + 3 c = − 14 a = − 14 − ( 6 b + 3 c ) [ Subtract ( 6 b + 3 c ) from both sides ] a = − 14 − 6 b − 3 c Substitute a = − 14 − 6 b − 3 c in the equation 2 a + b − 2 c = − 8 . 2 a + b − 2 c = − 8 2 ( − 14 − 6 b − 3 c ) + b − 2 c = − 8 [ Substitute a ] − 28 − 12 b − 6 c + b − 2 c = − 8 − 11 b − 8 c = − 8 + 28 [ Add − 28 on both sides ] − 11 b − 8 c = 20 ......... ( 1 ) Substitute a = − 14 − 6 b − 3 c in the equation − 3 a + 2 b + c = − 8 . − 3 a + 2 b + c = − 8 − 3 ( − 14 − 6 b − 3 c ) + 2 b + c = − 8 [ Substitute a ] 42 + 18 b + 9 c + 2 b + c = − 8 18 b + 9 c + 2 b + c = − 8 − 42 [ Subtract 42 from both sides ] 20 b + 10 c = − 50 10 ( 2 b + c ) = − 50 2 b + c = − 5 [ Divide by 10 on both side ] Solve 2 b + c = − 5 for c as follows. 2 b + c = − 5 c = − 5 − 2 b [ Subtract 2 b from both sides ] Substitute c = − 5 − 2 b in the equation (1)

College Algebra & Trigonometry - Standalone book

1st Edition

ISBN: 9780078035623

Author: Julie Miller, Donna Gerken

Publisher: McGraw-Hill Education

See similar textbooks

Videos

Question

Chapter 9, Problem 8T

To determine

To solve: The below system of equations. If the system does not have one unique solution, also state whether the system is inconsistent or whether the equations are dependent.

a+6b+3c=−142a+b−2c=−8−3a+2b+c=−8

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9, Problem 7T

Chapter 9, Problem 9T

Students have asked these similar questions

Determine whether it's true or false and the reasoning is needed

1. (20 pts) Determine whether the following statements are true (T) or false (F)? (A reasoning is required.) (1) Let V be the set of all ordered pairs of real numbers. Consider the following addition and scalar multiplication operations on u = u= (u1, u2) and v = (v1, v2): u + v = (U₁ + V₁, U₂ + v₂), ku = (ku₁, u₂). Is V a vector space under the above operations? U2 (2) The set Mmxn of all m×n matrices with the usual operations of addition and scalar multiplication is a vector space. α (3) The dimension of the vector space of all matrices A = [a b] in R2×2 with a+d=0 is 4. (4) The coordinate vector of p(x) = 2-x+x² in P3 relative to the basis S = {1, 1+x, x + x2} is [4 -2 1]. (5) If a 6×4 matrix A has a rank 3, then the dimension of N(A) is 3.

5. (20%) The linear transformation L: P3 → P2 defined by L(f(x)) = f'(x)+ f(0). (a) Find the representing matrix A of L with respect to the ordered basis {x2, x, 1} for P3, and the ordered basis {2,1 - x} for P2. (b) Find the coordinates of the f(x) = 2x² +2 in P3 with respect to the ordered basis {x2,-x, 1}, and find the coordinates of L(f(x)) with respect to the ordered basis {2,1-x}

Chapter 9 Solutions

College Algebra & Trigonometry - Standalone book

Ch. 9.1 - For Exercises R.1-R.4, solve the equation. R.1...Ch. 9.1 - Prob. R.2PE Ch. 9.1 - For Exercises R.1-R.4, solve the equation. R.3...Ch. 9.1 - Prob. R.4PE Ch. 9.1 - Graph the equation and identify the x and y-...Ch. 9.1 - Prob. R.6PE Ch. 9.1 - Prob. 1PE Ch. 9.1 - Prob. 2PE Ch. 9.1 - Prob. 3PE Ch. 9.1 - Prob. 4PE

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The below system of equations. If the system does not have one unique solution, also state whether the system is inconsistent or whether the equations are dependent. a + 6 b + 3 c = − 14 2 a + b − 2 c = − 8 − 3 a + 2 b + c = − 8

Solution Summary: The author explains how to solve the following system of equations. If the system doesn't have one unique solution, state whether it's inconsistent or dependent.

Videos

To solve: The below system of equations. If the system does not have one unique solution, also state whether the system is inconsistent or whether the equations are dependent.

a+6b+3c=−142a+b−2c=−8−3a+2b+c=−8

Want to see the full answer?

Chapter 9 Solutions

The below system of equations. If the system does not have one unique solution, also state whether the system is inconsistent or whether the equations are dependent. a + 6 b + 3 c = − 14 2 a + b − 2 c = − 8 − 3 a + 2 b + c = − 8

Solution Summary: The author explains how to solve the following system of equations. If the system doesn't have one unique solution, state whether it's inconsistent or dependent.

Videos

To solve: The below system of equations. If the system does not have one unique solution, also state whether the system is inconsistent or whether the equations are dependent. a+6b+3c=−142a+b−2c=−8−3a+2b+c=−8

Want to see the full answer?

Chapter 9 Solutions

To solve: The below system of equations. If the system does not have one unique solution, also state whether the system is inconsistent or whether the equations are dependent.

a+6b+3c=−142a+b−2c=−8−3a+2b+c=−8