/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q44E If聽聽for a 10 x 10 matrix A, th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q44E (page 164)

Iffor a 10 x 10 matrix A, then the inequalityrankA猢�5must hold.

Short Answer

Expert verified

The above statement is true.

If for a 10 x 10 matrix A, then the inequality rank (A) 鈮� 5 must hold.

Step by step solution

01

Mentioning the concept

If A and B are two matrices of order n x n then, we have

rank(A)+rank(B)-n猢�rank(AB) (1)

02

Finding the rank of a matrix A of order 10 x 10

We have given a matrix A of order 10 x 10 such thatA2=0

Let us take matrix A = matrix B

鈬�rank(A)=rank(B)and rank(AB) = rank(A2)

鈭�A2=0鈬�rank(A2)=0

Therefore, from inequality (1), we have

rank(A)+rank(A)-10猢�rank(A2)鈬�2rank(A)-10猢�0鈬�rank(A)猢�5

03

Final Answer

If A2=0for a 10 x 10 matrix A, then the inequality rank (A) 鈮� 5 must hold.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Problem 46 through 55, Find all the cubics through the given points. You may use the results from Exercises 44 and 45 throughout. If there is a unique cubic, make a rough sketch of it. If there are infinitely many cubics, sketch two of them.

(0,0),(1,0),(2,0),(3,0),(4,0),(0,1),(0,2),(0,3),(1,1)

Express the line Lin 鈩�3 spanned by the vector[111]as the image of a matrix Aand as the kernel of a matrix B.

In Exercise 44 through 61, consider the problem of fitting a conic throughm given pointsP1(x1,y1),.......,Pm(xm,ym) in the plane. A conic is a curve in 鈩�2that can be described by an equation of the formf(x,y)=c1+c2x+c3y+c4x2+c5xy+c6y2+c7x3+c8x2y+c9xy2+c10y3=0 , where at least one of the coefficientsci is non-zero. If kis any nonzero constant, then the equationsf(x,y)=0 andkf(x,y)=0 define the same cubic.

45. Show that the cubic through the points(0,0),(1,0),(2,0),(3,0),(0,1),(0,2)补苍诲鈥�(0,3) can be described by equations of the form c5xy+c8x2y+c9xy2=0, where at least one of the coefficientsc5,c8,补苍诲鈥�c9 is nonzero. Alternatively, this equation can be written asxy(c5+c8x+c9y)=0 . Describe these cubic geometrically.

Give an example of a linear transformation whose kernel is the plane x+2y+3z=0in鈩�3.

Give an example of a noninvertible function Ffrom鈩�to 鈩浓划with

im(f)=鈩�
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.