/*! 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} Q32E If an n 脳 n matrix A is similar... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q32E (page 164)

If an n 脳 n matrix A is similar to matrix B, thenA+7In must be similar toB+7In.

Short Answer

Expert verified

The above statement is true.

If an n 脳 n matrix A is similar to matrix B, then A+7Inmust be similar toB+7In.

Step by step solution

01

Definition of similar matrix

Let A and B are two square matrices, the matrix A is said to be similar to matrix B if there exists an invertible matrix P such that

B=P-1AP

02

Mentioning the concept

Since matrix A is similar to matrix B then there exists an invertible matrix P such that

B=P-1AP

Now, we have to show that the matrix A+7Inmust be similar to the matrixB+7In.

We have

P-1(A+7In)P=P-1AP+P-17InP鈬�P-1(A+7In)P=B+7In(鈭�P-1AP=B)

This implies that there exists an invertible matrix P such that

P-1(A+7In)P=B+In

Hence, the matrix A+7]nmust be similar to the matrixB+7In.

03

Final Answer

If an n 脳 n matrix A is similar to matrix B, then A+7Inmust be similar toB+7In. as there exists an invertible matrix P such thatP-1(A+7In)P=B+In.

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

Question: In Exercises 1 through 20, find the redundant column vectors of the given matrix A 鈥渂y inspection.鈥� Then find a basis of the image of A and a basis of the kernel of A.

16.[1-20-100015000001]

Consider the plane x1+2x2+x3=0. Find a basis of this plane such that [x鈫�]B=[2-1]forx鈫�=[1-11].

We are told that a certain5脳5 matrixA can be written as

A=BC,

where Bis 5脳4andC is 4脳5. Explain how you know thatA is not invertible.

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)

In Exercise 44 through 61, consider the problem of fitting a conic throughmgiven points P1(x1,y1),.......,Pm(xm,ym)in the plane. A conic is a curve in 鈩�2that can be described by an equation of the form , f(x,y)=c1+c2x+c3y+c4x2+c5xy+c6y2+c7x3+c8x2y+c9xy2+c10y3=0where at least one of the coefficientsciis non zero. If is any nonzero constant, then the equationsf(x,y)=0and kf(x,y)=0define the same cubic.

44. Show that the cubic through the points(0,0),(1,0),(2,0),(0,1),and(0,2)can be described by equations of the form c5xy+c7(x3鈭�3x2+2x)+c8x2y+c9xy2+c10(y3鈭�3y2+2y)=0, where at least one of the coefficients is nonzero. Alternatively, this equation can be written as .c7x(x鈭�1)(x鈭�2)+c10y(y鈭�1)(y鈭�2)+xy(c5+c8x+c9y)=0
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.