Question: 4. A matrix will be singular if any row is a linear combination of the other rows, or if any column is a linear combination

4. A matrix will be singular if any row is a linear combination of the other rows, or if any column is a linear combination of the other columns. (a) Explain in geometric terms Why both of these are true. (b) Demonstrate that Gaussian elimination must yield a zero row in both cases. (c) Explain why both conditions are not only su'icz'ent for singularity, but are also necessary; that is, any singular matrix must have at least one linearly dependent row and one linearly dependent column. This implies that if any row is a linear combination of others, then at least one column must also be linearly dependent, and vice versa

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!

Answer Question A matrix will be singular if any row is a linear combination of the other rows, or if any column is a linear combination of the other columns. (a) Explain in geometric terms Why both...

please provide hand written solution Question 4 -2 -6 24 -20 0 2 Let A = -2 -3 9 -14 0 5 4 9 -33 34 3 -13 -2 -3 9 -14 -3 11 It is given that the reduced row-echelon forms of A and AT are respectively...

Design and Implement an Algorithm in Java to solve the following problem in solving linear equations using the Gaussian Elimination method. Definition: A system of linear equations can be placed into...

Need help with problem 1, 2, 3, and 4. 1. Verify that a matrix multiplied by a column vector is simply a linear combination of the columns of the matrix. Namely, if the columns of the matrix A are...

6. Write a function in numpy that takes two arbitrary shape matrices and calculates the product by the outer product method. Make sure it checks whether their shapes are compatible. 7. Calculate the...

This needs to be done in python. 0. Create a new markdown cell below and type in the answers. 1. Write a function that takes in two vectors and returns their inner product. Use a loop or nditer, not...

8. Verify that a matrix multiplied by a column vector is simply a linear combination of the columns of the matrix. Namely, if the columns of the matrix A are a_1, a_2, .. a_n and the vector x is...

For all MATLAB codes written, appropriate comments are re- quired. Solutions must be uploaded in PDF format to Canvas. 1. A common problem in practical computations is to take an array and sort it in...

Consider the following two partitions of an (m x n) matrix A: a1] a12 aIn a21 a22 . . . a2n A = [ Al A2 .. An] am1 am2 Umn- alla a1 1 a12 . . . ain at a21 a22 . . . a2n A = = * . . . . . . . T ami...

Solve Problem 4.116 for a = 4.5 ft. P4.116 The 18-ft pole ABC is acted upon by a 210-lb force as shown. The pole is held by a ball-and-socket joint at A and by two cables BD and BE. For a = 9 ft,...

Explain carefully the arbitrage opportunities in Problem 10.16 if the American put price is greater than the calculated upper bound.

Question content area Part 1 The bubble that results from an informational cascade can in fact be rational since Part 2 A . investors early in the chain may have obtained information that increases...

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...