Question: Prove that a 2 Ã 2 matrix is reducible if and only if a 12 = 0 or a 21 = 0. A12 A =

Prove that a 2 × 2 matrix
A12 A = a22 a21 И22

is reducible if and only if a12 = 0 or a21 = 0.

A12 A = a22 a21 22

Step by Step Solution

★★★★★

3.37 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

By the discussion preceding Theorem 437 a matrix A is reduc... 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 (2 attachments)

PDF file Icon

1623_606b0df16fcf0_699284.pdf

180 KBs PDF File

Word file Icon

1623_606b0df16fcf0_699284.docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

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

Q:

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

Q:

(a) Prove that an orthogonal 2 Ã 2 matrix must have the form where is a unit vector. (b) Using part (a), show that every orthogonal 2 Ã 2 matrix is of the form where 0 ¤ u...

Q:

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Q:

1 2 3 4 OT Using a cofactor expansion across the first row, find 7 8 (Hint the cofactor expansion across the first row is All A12 p13 all A12 013 All 12 213 + a13 a21 a22 A23 - a12 a21 122 a23 a31...

Q:

I need help with this homework. Need Program design and the C++ code. Pr ogr amming Assignment: Abstract Data Type - Matrix The purpose of this course is 1. identification of the appropriate ABSTRACT...

Q:

I need help with this homework. Need Program design and the C++ code. Pr ogr amming Assignment: Abstract Data Type - Matrix The purpose of this course is 1. identification of the appropriate ABSTRACT...

Q:

I need help in answering these 2 questions on MIPS assembly language. Problem1.ASM ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Create some null terminated strings to use .data...

Q:

Need help with this homework. I need to do the design and the c++ code. Please try to type the answer. Thank you Pr ogr amming Assignment: Abstract Data Type - Matrix The purpose of this course is 1....

Q:

Need help with this homework. Can you read the question and help me to do the coding and also, can you explain what you are doing in each line of this code? Also can you please type the answer. Thank...

Q:

Haas Plastics manufactures custom park furniture and signage from recycled plastics (primarily shredded milk jugs). Many of the companys customers are municipalities that are required by law to...

Q:

You have been given the following information for Corkys Bedding Corp.: a. Net sales = $11,250,000 b. Cost of goods sold = $7,500,000; c. Other operating expenses = $250,000; d. Addition to retained...

Q:

Clarissa wants to fund a growing perpetuity that will pay $ 1 1 comma 0 0 0 $ 1 1 , 0 0 0 per year to a local museum, starting next year. She wants the annual amount paid to the museum to grow by 6 6...

Q:

What is the 75th percentile for GPA in Appendix Data Set? (This is the point below which 75% of the observations are expected to fall.)

Q:

What is the lifetime risk (from age 15 to age 70) of testicular cancer for men with age at surgery = 15, assuming that the incidence rate remains constant over time? Assume that all men do not die of...

Q:

What is the probability that a 40-year-old woman will develop colon cancer over the next 5 years? Cancer Data from the Surveillance Epidemiology and End Results (SEER) registry provides incidence...

Q:

What is the probability that a 40-year-old woman will develop colon cancer over the next 20 years (i.e., from age 40.0 to age 59.9)? Cancer Data from the Surveillance Epidemiology and End Results...

Q:

In a discount interest loan, you pay the interest payment up front. For example, if a 1-year loan is stated as $48,000 and the interest rate is 7.75%, the borrower "pays" .0775 times $48,000 = $3,720...

Q:

Test 2 (Chapter 3 and 4) 25 points possible 1/25 answered Question 6 Next

Q:

Given the following information: \ table [ [ Job , Arrival Time,CPU Cycle ] , [ A , 0 , 1 2 ] , [ B , 2 , 2 ] , [ C , 3 , 1 0 ] , [ D , 6 , 7 ] , [ E , 1 0 , 3 ] ] Calculate which jobs will have...