Question: Construct a (simple ?) (2 2) matrix A and find one vector b such that system Ax = b has no solutions at all, but

Construct a (simple ?) (2 2) matrix A and find one vector b such that system Ax = b has no solutions at all, but system Ax = 0 has infinitely many solutions. Justify your claims about the number of solutions.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Construct a (simple ?) (2 2) matrix A such that for any vector b R2 system Ax = b has exactly one solution, and Ax = 0 has only the trivial solutiion. Justify your claims about the number of...

Function and Vector operations. Define 2 vectors and name them vec 1 and vec 2 both with 3 elements. vec 1 = [ 1 , 2 , 3 ] and vec 2 = [ 4 , 5 , 6 ] Calculate the dot product and the cross product of...

1. Determine if the following system has a nontrivial solution, and explain what the solution is. -5x1 + 7x2+ 9x3 = 0 X1 - 2x3 + 6*3 = 0 2. Construct a 3-by-3 nonzero matrix A such that the vector is...

. Write a MATLAB function x=GEPP(A, b), with input the matrix A, right hand side vector b and output the solution vector x. (a) Add the partial pivoting procedure to the Gaussian elimination code, ....

0 - 1 0 Let v1 = _1 , v2 = 0 , and v3 = 1 . Does {V1,V2,V3} span R4? Why or why not? 1 1 0 Choose the correct answer below. {:5 A- Yes. Any vector in R4 except the zero vector can be written as a...

Let A be a 3x3 matrix of coefficients of a linear system of equations A.x = b where b is some vector in R3. Assume that we know that x0 = (1, 2, 3 ) is a solution of that system, and we also know...

3. (Applying LU and LUP decompositions, 16pt) In this problem, we'll use the LU/LUP decomposition to solve a linear system of equations. a) [4pt] For A [11-15-13 -13 5;14 -8 16 -3 -17;-14 1 16 14...

please use matlab and use the given work The original csolve code is as follows A hint to how this problem could run Submit your m-file and a diary that shows how you tested the code. Modify csolve.m...

3. (Applying LU and LUP decompositions, 16pt) In this problem, we'll use the LU/LUP decomposition to solve a linear system of equations. a) [4pt] For A= [11-15-13 -13 5:14 -8 16-3-17;-14 1 16 14...

Write a script to create a matrix ? b a r ( ? b a r ( A ) ) i n R n n with ninN, where ? b a r ( ? b a r ( A ) ) is: ? b a r ( ? b a r ( A ) ) = [ 4 - 1 0 0 d o t s 0 0 0 - 1 - 1 4 - 1 0 d o t s 0 0...

At December 31. 2022, Pronghorn Corporation reported the following plant assets. Land $3.498,000 Buildings $26,630,000 Less: Accumulated depreciation-buildings 13,904,550 12.725,450 Equipment...

Show that, under the hypothesis of Corollary 11.2, if y2 is the solution to y" = p(x)y' + q(x)y and y2(a) = y2(b) = 0, then y2 0.

Which of the following may represent a DISADVANTAGE to "debt financing"? Question 6 options: a) Debt must be paid at maturity. b) Potential loss of corporate control c) Interest paid is deductible...

2023 1040 form 1.Phillip and Claire are married and file a joint return. Phillip is self-employed as a real estate agent, and Claire is a flight attendant. Phillip and Claire have three dependent...