1.2.12 (a) Explain why every linear system over R has either zero solutions,one unique solution, or infinitely many solutions.(b) Why doesn't this contradict the fact that the system of equationsx? – y = 1-x+ 2y = 3has exactly two solutions?

Answered: Image /qna-images/answer/bae29054-0b29-4b04-a8ef-cdcdb166f71f.jpg

Answered: 1.2.12 (a) Explain why every linear…

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

Similar questions

13
1. True or False? Justify all answers. a. A system of 4 linear equations in 3 unknowns has no solutions. True or False, Justify the answer. b. There exist three planes in R³ which intersect in exactly three points. True or False, Justify the answer. c. If u, v and w are linearly dependent, then w can be written as linear combination of u and v. True or False, Justify the answer. d. Let A be a 4 x 5 matrix. Then the column vectors of A are linearly dependent. True or False, Justify the answer. e. f. If u is in span{v, w} then u is in span{v + w, w - v}. True or False, Justify the answer. let A, B be two matrices. If (A - B)² = A² - 2AB + B², then AB = BA. True or False, Justify the answer. g. If A and B are symmetric matrices, then AB is a symmetric matrix. True or False, Justify the answer.
1) Write down the linear system of equations for the coefficients of a quadratic polynomial f(x) = ax2+bx+c, that would interpolate the points (-2, 1), (-1, 4), (1, 2) and (3, -1). 2) Explain why the system you found in (a) is inconsistent (so no such polynomial exists). 3) Find the normal equation for the system you found in (a). 4) Find the polynomial of degree 2 that best fits the points in (a).
Prove that the following statement is FALSE: A system of four linear equations in three unknowns is always inconsistent. Proof idea: Start by recalling that inconsistent means that there is no solution. Now write down a specific example of a system of four equations in variables x1, x2, x3 that WILL have a solution. Hint: Show that it does have a solution.
How can x-5= x + 6 be set up as a system of equations? O 2y + x = -10 3y + x = 18 O2y + 2x = -10 3y + 3x = 18 O2y-x= -10 3y - x = 18 O2y-2x = -10 3y - 3x = 18

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

1.2.12 (a) Explain why every linear system over R has either zero solutions, one unique solution, or infinitely many solutions. (b) Why doesn't this contradict the fact that the system of equations x² – y = 1 x+ 2y = 3 has exactly two solutions?