Question: Prove that a 2 2 matrix A is reducible if and only if a12a21 = 0.

Prove that a 2 × 2 matrix A is reducible if and only if a12a21 = 0.

Step by Step Solution

★★★★★

3.45 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

There are only two possible partitions of the ... View full answer

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

Document Format (1 attachment)

Word file Icon

949-M-L-A-E (877).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Prove that a 2 Ã 2 matrix is reducible if and only if a 12 = 0 or a 21 = 0. A12 A = a22 a21 22

Q:

Prove Theorem 17.7. For polynomials in F[x], (a) Every nonzero polynomial of degree

Q:

(a) Show that if Is a 2 à 2 diagonal matrix with α b, then the only matrices that commute (under matrix multiplication) with D are other 2 à 2 diagonal matrices. (b) What...

Q:

(a) Prove that any 2 2 matrix of rank 1 can be written in the form A = uvT where u, v R2 are non-zero column vectors. (b) Which rank one matrices correspond to orthogonal projection onto a...

Q:

X Course Hero Differential Equations and Linear X G Determine all values of the const x M (no subject) - sylviaabdelmasih@ x...

Q:

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Q:

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

Q:

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

Q:

(b The variances of random variables Y and Z are 0.36 and 16 respectively, the covariance Cov(Y, Z) = 2. (i) Write down the variance-covariance matrix A of (Y, Z) vector. (ii) Verify that the...

Q:

HEY CAN YOU HELP ME SOLVE THE FOLLOWING QUESTIONS: 63, 65, 73, 81, 82, 83 5.3 Diagonalization of Matrices 323 57. [_7 3]: ([:] . ): 43 74. Find a 2 x 2 matrix having eigenvalues 7 and -4, with 58. 2...

Q:

Find the Thevenin equivalent of the circuit in figure at the terminals A-B. -O A 3 kn 2 kn 4 Vx 1 kn 1000 -O B

Q:

What is involved in the company analysis phase of market analysis in Figure 1-1?

Q:

Which of the following gives a preferred shareholder the right to a particular dollar amount from the assets of the corporation that is superior to any right that common shareholders have in the...

Q:

Determine the equilibrium level of national income using an aggregate expenditure chart or graph.

Q:

Let C = [Cij] be an n x n positive definite symmetric matrix and let V be an n-dimensional vector space with ordered basis S = {u1, u2,... un}. For v = a1u1+ a2u2+...+anun and w = b1u1+b2u2+ ... +...

Q:

In the Euclidean space Rn with the standard inner product, prove that (u, v) = uTv.

Q:

Consider Euclidean space R4 with the standard inner product and let (a) Prove that the set W consisting of all vectors in R4 that are orthogonal to both u1 and u2 is a subspace of R4. (b) Find a...

Q:

Blue Moose Home Builders is considering investing $450,000 in a project that is expected to generate the following net cash flows: Year Cash Flow Year 1 $300,000 Year 2 $400,000 Year 3 $425,000 Year...

Q:

Show work 1.A respected analyst forecasts that the return of the S&P 500 Index portfolio over the coming year will be 10%. The one-year T-bill rate is 5%. Examination of recent returns of the S&P 500...

Q:

Future Prices $60.04 per barrel. Suppose futures prices change each day as follows. a. What is the marking-to-market profit or loss (in dollars) that you will have on each date? b. What is your total...