Question

Use the matrix method (together with elementary row transformation) to solve the following y + z = 2 2x + 3z = 5 x + y + z = 3 A. The determinant is not zero and the system has no solution. B. The determinant is not zero and the system has unique solution. C. The determinant is not zero and the system has infinitely number of solutions. Choose the correct option for the statements: a. All A, B and C b. Only C 

          Use the matrix method (together with elementary row transformation) to solve the following
y + z = 2
2x + 3z = 5
x + y + z = 3
A. The determinant is not zero and the system has no solution.
B. The determinant is not zero and the system has unique solution.
C. The determinant is not zero and the system has infinitely number of solutions.
Choose the correct option for the statements:
a. All A, B and C
b. Only C
Show more…
Use the matrix method (together with elementary row transformation) to solve the following y + z = 2 2x + 3z = 5 x + y + z = 3 A. The determinant is not zero and the system has no solution. B. The determinant is not zero and the system has unique solution. C. The determinant is not zero and the system has infinitely number of solutions. Choose the correct option for the statements: a. All A, B and C b. Only C

Added by Brian J.

Close

Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
Use the matrix method (together with elementary row transformation) to solve the following: y + z = 2 2x + 3z = 5 x + y + z = 3 A. The determinant is not zero and the system has no solution. B. The determinant is not zero and the system has a unique solution. C. The determinant is not zero and the system has an infinitely number of solutions. Choose the correct option for the statements: a. All A, B, and C b. Only C Use the matrix method (together with elementary row transformation) to solve the following: 2 + 3z = 5 y + 2 = 3 A. The determinant is not zero and the system has no solution. B. The determinant is not zero and the system has a unique solution. C. The determinant is not zero and the system has an infinitely number of solutions. Choose the correct option for the statements: a. All A, B, and C b. Only C
Close icon
Play audio
Feedback
Powered by NumerAI
Kathleen Carty Jennifer Stoner
Ivan Kochetkov verified

Donna Densmore and 82 other subject Precalculus educators are ready to help you.

Ask a new question
*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs
*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.
*

Recommended Videos

-
use-the-determinant-of-the-coefficient-matrix-to-determine-whether-the-system-of-linear-equations-has-a-unique-solution-2x1-3x2-3x3-24-6x1-6x2-12x3-97-12x1-9x2-x3-5-the-system-has-a-unique-s-11296

Use the determinant of the coefficient matrix to determine whether the system of linear equations has a unique solution. 2x1 + 3x2 + 3x3 = 24 6x1 + 6x2 + 12x3 = 97 12x1 + 9x2 - x3 = -5 The system has a unique solution because the determinant of the coefficient matrix is nonzero. The system does not have a unique solution because the determinant of the coefficient matrix is zero. The system does not have a unique solution because the determinant of the coefficient matrix is nonzero. The system does not have a unique solution because the determinant of the coefficient matrix is zero. If the system has a unique solution, use Cramer's Rule to find the solution. (If not possible, enter IMPOSSIBLE.) (x1, x2, x3) =

Donna D.
use-the-determinant-of-the-coefficient-matrix-to-determine-whether-the-system-of-linear-equations-has-a-unique-solution-x1-x2-x3-4-2x1-x2-x3-6-4x1-3x2-3x3-the-system-has-a-unique-solution-be-69016

'Use the determinant of the coefficient matrix to determine whether the system of linear equations has a unique solution: X1 - X2 + X3 = 4 2x1 X2 + X3 = 6 4x1 - 3X2 3X3 The system has a unique solution because the determinant of the coefficient matrix is nonzero. The system has a unique solution because the determinant of the coefficient matrix is zero. The system does not have a unique solution because the determinant of the coefficient matrix is nonzero. The system does not have a unique solution because the determinant of the coefficient matrix is zero.'

Sri K.
solve-the-following-system-using-augmented-matrix-methods-2x15x25x333-2x10x23x316-7x10x29x347-a-the-initial-matrix-is-b-first-perform-the-row-operation-12r1r112r1r1-the-resulting-matrix-is-c-99569

Solve the following system using augmented matrix methods: 2x1 - 5x2 + 5x3 = -33 2x1 + 0x2 + 3x3 = -16 7x1 + 0x2 + 9x3 = -47 (a) The initial matrix is: [2 -5 5 | -33] [2 0 3 | -16] [7 0 9 | -47] (b) First, perform the Row Operation 12R1 → R1. The resulting matrix is: [24 -60 60 | -396] [2 0 3 | -16] [7 0 9 | -47] (c) Next, perform the operations -2R1 + R2 → R2 -7R1 + R3 → R3. The resulting matrix is: [24 -60 60 | -396] [0 120 -117 | 764] [0 420 -423 | 2719] (d) Finish simplifying the augmented matrix down to reduced row echelon form. The reduced matrix is: [1 0 0 | -3] [0 1 0 | 5] [0 0 1 | -7] Remember: This matrix must be simplified all the way to reduced form. (e) How many solutions does the system have? If infinitely many, enter "Infinity". The system has a unique solution. (f) What are the solutions to the system? x1 = -3 x2 = 5 x3 = -7 Note: If there are no solutions, write "No Solution" or "None" for each answer. If there are infinitely many solutions, and the solution set describes a line (that is, if there is only one free variable), set x3 = t and solve for the remaining variables in terms of t. If there are infinitely many solutions, and the solution set describes a plane (that is, if the solution set has two free variables), set the variables x3 = t and x2 = s, and then solve for x1 in terms of s and t.

Zhumagali S.
*

Recommended Textbooks

-
Precalculus with Limits

Precalculus with Limits

Ron Larson 2nd Edition
achievement 1,819 solutions
Precalculus

Precalculus

Robert Blitzer 5th Edition
achievement 1,175 solutions
Precalculus

Precalculus

Jay Abramson 1st Edition
achievement 1,155 solutions
*

Transcript

-
00:01 We want to use kramer's rule to see if this matrix has a coefficient matrix has a solution or not.
00:08 And to do that, we need to get the determinant.
00:10 So i wrote down the coefficient matrix here, and i took the determinant, and that determinant was 168.
00:17 Therefore, that tells me it does have a solution.
00:20 So now we're going to use kramer's rule to find the actual solutions.
00:25 To do that, i'm going to take the answer matrix, and i'm going to put that in place.
00:30 Place of x, leave everything else in there, and that's going to give me the determinant about x.
00:36 So i'm going to pause and get that on my calculator.
00:39 When i did, i got that on my calculator, did the determinant, and got a value of 84.
00:44 Now i'm going to do the same thing with my y column.
00:47 I'm going to put the answers here in the y column and find its determinant.
00:53 Now when i did that, i put the two, six, and twelve back in place of my x column, and only replaced three, six, and nine with those values.
01:02 So that's going to be called the determinant about y and that gave me a value of negative 56.
01:07 And lastly, we're going to maintain the x and y column just as they are, but now i'm going to take the answer matrix and put it in place of the z column.
01:17 So i'm going to pause and get that value.
01:20 Upon placing those values, i got the determinant about z, which i got 1344.
01:27 Now, so what are our answers? our answer for x is going to be the determinant...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade

Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever