For all the following linear systems(i) Write the following linear systems in matrix notation Ax = b. Then, using the formula forA-1 above, find the unique solution x = (x1, x2)", or determine that the system has infinitelymany solutions (explain what they are), or that is has no solution.(ii) Graph each equation in the system, in the x1- 12 plane, and determine graphically whetherthe system has one solution, infinitely many solutions or none. 4.x1 + x2 = 0 , 4x1 – 3x2 = -12

Answered: Image /qna-images/answer/1c422624-b748-4f53-83a5-02e836d548c0.jpg

For all the following linear systems i) Write the following linear systems in matrix notation Ax = b. Then, using the formula for 1-1 above, find the unique solution x = (x1, x2)", or determine that the system has infinitely nany solutions (explain what they are), or that is has no solution. ii) Graph each equation in the system, in the xı–x2 plane, and determine graphically whether he system has one solution, infinitely many solutions or none.

For all the following linear systems i) Write the following linear systems in matrix notation Ax = b. Then, using the formula for 1-1 above, find the unique solution x = (x1, x2)", or determine that the system has infinitely nany solutions (explain what they are), or that is has no solution. ii) Graph each equation in the system, in the xı–x2 plane, and determine graphically whether he system has one solution, infinitely many solutions or none.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Find the solution to the system of equations using matrix inversion: - 2y + z = - 5 5х + 5у + 52 –…

A: Given that -2y+z=-5 5x+5y+5z=-40 -x-2y+z=4

Q: Find the augmented matrix for the following system of linear equations: 3x + + 4y + 7z 26 5х + 7y +…

Q: (7- 8)2 | /8-ん (e-)」ade-)|I/8-ん Hence, 2By < 1, (7 – 6)2 vhich can be written as |a(y – 8) + 3||y –…

A: I have only deducted the green part as per your request.

Q: Write the following linear system in matrix form: 2x1 + 3x2 = 0 3x2 + x3 = 0 2x1 − x2 = 0

A: Given system of linear equations : 2x1 + 3x2 = 03x2 + x3 = 02x1 − x2 = 0

Q: Find the augmented matrix for the following system of linear equations. 4x1 + 7x3 = -7 7x — Зх, +…

Q: Find the solution set of system of linear equations represented by the augmented matrix:

Q: Consider the following system of linear equations for four real variables x1, x2, X3, X4: x2 + x3 –…

A: x2+x3-2x4=-3x1+2x2-x3=22x1+4x2+x3-3x4=-2x1-4x2-7x3-x4=-1011-212-10241-31-4-7-1x1x2x3x4=-32-2-19Let…

Q: Write the following system of equations in matrix form and show that it is linearly independent. -3x…

A: Given: The system of equations -3x + 2y - z = 14 -x -y -z = 0 x + 10y - 3z = 2…

Q: Find the augmented matrix for the following system of linear equations: -5x 12у + 51z 46 - -12x 29у…

A: To find the augmented matrix for the below system of linear equations.…

Q: Find the augmented matrix of the following system of linear equations: X2 + x4 = 2 3x1 – x2 = -1 %3D

A: NOTE: Refresh your page if you can't see any equations. . given equations are . rewrite the system…

Question

For all the following linear systems
(i) Write the following linear systems in matrix notation Ax = b. Then, using the formula for
A-1 above, find the unique solution x = (x1, x2)", or determine that the system has infinitely
many solutions (explain what they are), or that is has no solution.
(ii) Graph each equation in the system, in the x1- 12 plane, and determine graphically whether
the system has one solution, infinitely many solutions or none.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Paths and Circuits$

Learn more about

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

Similar questions

Write the following system as a vector equation involving a linear combination of vectors and solve for the unknowns. 5x12x2x3 = 2 4x₁ + 3x3 = −1
Consider the following system of linear equations. 2x+4y=6 6x +14y=22 Solve the system by completing the steps below to produce a reduced row-echelon form. R₁ and R₂ denote the first and second rows, respectively. The arrow notation (→) means the expression/matrix on the left becomes the expression/matrix on the right once the row operations are performed. (a) For each step below, enter the coefficient for the row operation. The first matrix in Step 1 is the augmented matrix for the given system of equations. Step 1: 4 6 14 i 22 2 Step 2: 1 2 6 14 i 22 Step 3: 6 1 2 3 [31] 0 4 1 x = 3 2 (b) Give the solution. =0 D-R, R₁ R₁ + R₂ R₂ y = 0 R₂ R₂ 6 Step 4: Enter the coefficient for the row operations and the missing entries in the resulting matrix. []. R₂ + R₁ → R₁ 2 12 3 22 12 ! 3 10 0 4 2 00 X 0.0
please, solve it asap!
Solve the linear system corresponding to the following augmented matrix: 3 6 24 2 3 11 O A. (0,0) OB. (-2,-5) O C. (5,-2) O D. (-2,5)
HELP ME PLS
Write the system as a vector equation or matrix equation as indicated. Write the following system as a vector equation involving a linear combination of vectors. 3X₁ - 4X₂ - X3 = -6 6x₁ + 3x3 = -6 X1 -6 -X₂0 3 0×[³] + [1] + [ ] - [ ] O [1] 3x2 4*2-2 -6 [x3] 0 ***
When writing the following linear system of equations in the matrix form Ax = b -5x1 + 2x2 = -4 -2x₁ - 5x2 = −1 a. What is the matrix A?
Find the augmented matrix for the following system of linear equations: -5x 16у + 4x 12y + + 97y -4 31x -31 || |||| | +
Write the following linear systems in augmented matrix form, wherethe variables are ordered using the regular alphabetical order. 7 − B + 4C − 3D = A + 2 − 3B − 5C5B + 9 = −1 + 2A + 6B + 6C + 2D
Rewrite the following system of linear equations as (a) a vector equation and (b) an augmented matrix. (c) Find and write the solution in general form. -I1 + X2 3x1 I1 + 2x2 + 5х3 + 3х4 6x3 3x4 4x3 + X4 2 = 6 0 =
I. Consider the following linear system: 3x1 + 9x2 + 3x3 = 6 2x1 — 2х1 — 4x2 X3 = 12 = -8 We can view this system as a matrix equation: 3 9 31 0 -1 2 12 -2 -4 Which has the form: Ax X = B To solve the original system, we can solve this equation for X by multiplying by A-1: A-1x (A x X) = A-! × B (A-1 × A) × X = A-1 × B Iz x X = A-1 × B X = A-1 x B Use the bottom equation to solve for X. Find A-1 for the matrix A and solve the original system by using A-1 and Bin the (1) equation below. X = A-1 x B (2] Use the matrix A² you just found to solve the system: 3x1 + 9x2 + 3x3 = 12 2x1 -2x1 – 4x2 X3 = 9 = -3
The vector (-1, 1, –3) is a solution of the linear system: X1 + 3x2 – 3x3 = 14 5x1 + 13x2 – 13x3 = 60 -xI - 2x2 + 2x3 = -9 %3D O True O False