Prove that the linear transformation S is invertible. Then find a formula for the inverse linear transformation,

Question:

Prove that the linear transformation S is invertible. Then find a formula for the inverse linear transformation, S-1, by employing a matrix inverse.
S: P1 → M1,2, S (a + bx) = [3a + b 2a + b]

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra

ISBN: 9780982406212

1st Edition

Authors: Jim Hefferon

See More Books

Question Posted: Jun 01, 2016 02:42 AM

See More Questions

(a) Prove that the linear transformation associated with the improper orthogonal matrix is a reflection through the line that makes an angle 1/2 Î¸ with the x-axis. (b) Show that the...
Let S22 be the set of 2 Ã 2 symmetric matrices. Verify that the linear transformation R is invertible and find R-1. R(E)- =(a b) + (2a 3b 2c)a + (a b+ c)a? R: S2 + P2, R %3D
Let S be the standard basis for Rn. Prove Theorem 8.6.2 by showing that the linear transformation T: V Rn that maps v V to its coordinate vector (v)s in Rn is an isomorphism.
In the Diffie-Hellman protocol, what happens if, x and y have the same value? That is, Alice and Bob have accidentally chosen the same number. Are the values of R1 and R2 the same? Are the values of...
You are evaluating two companies as possible investments. The two companies, similar in size, are commuter airlines that fly passengers across the United States of America. All other available...
1. Exercise 30.1 (Variants of the Stag Hunt) Consider variants of the n-hunter Stag Hunt. That is, there are n number of hunters. Only m hunters, with 2 m
Determine whether the following can be probability distributions of a random variable that can take on only the values of 0,1 , and 2 : (a) $f(0)=0.34 \quad f(1)=0.34$ and $f(2)=0.34$. (b)...
The Bango Toy Company produces several types of toys to seasonal demand. The forecast for the next six months in thousands of dollars is given below: A regular employee can produce $10,000 worth of...
Given the information answer the question below. Plant & machinery (at cost) Provision for depreciation of plant & machinery at 1 October Year 6 Bad debts (written off) 160,000 64,000 Sales 325...
The string of a conical pendulum is 50 cm long and the mass of the bob is 0.25 kg. Find the angle between the string and the horizontal when the tension in the string is six times the weight of the...
Find bases for the kernel and range of the linear transformation S below. c + c-d)+(3a- b+ Sc +2)(a+b+c-2)
The linear transformation R: M12 M21 is invertible. Use a matrix representation to determine a formula for the inverse linear transformation R-1: M21 M12. a +3b las a +11b
A certain LTI system has an input/ output relationship given by (a) Find the output autocorrelation, RYY (Ï), in terms of the input autocorrelation, RXX (Ï). (b) Find the output PSD, SYY...
List four differences between the accounting depreciation/amortization and Capital Cost Allowance methods for tax purposes. In Canada
P5.4. (DC, RFC and NRFC) The following data were taken from the financial statements of Chen Corporation for 2021 taxable year: Gross sales Sales returns Cost of goods sold Operating expenses...
1. During 2022, Hugh (an employee at General Motors) paid the following taxes. How much of these taxes would be deductible as an itemized deduction? Real estate property tax on Michigan...
my thesis is- Understanding the relationship between women's rights and human rights requires an analysis of interdependence; women's rights are an inherent component of human rights, and the state...
Will a VAT registered taxpayer have a VAT still due from his sales transaction with the government? Discuss and support your answer.
A fish at a pressure of 1.1 atm has its swim bladder inflated to an initial volume of 8.16 mL. If the fish starts swimming horizontally, its temperature increases from 20.0C to 22.0C as a result of...
Estimate a range for the optimal objective value for the following LPs: (a) Minimize z = 5x1 + 2x2 Subject to X1 - x2 3 2x1 + 3x2 5 X1, x2 0 (b) Maximize z = x1 + 5x2 + 3x3 Subject to X1 + 2x2 +...
True or false: If A and B are incidence matrices of the same size and coker A = coker 5. then the corresponding digraphs are equivalent.
(a) Explain why the incidence matrix for a disconnected graph can be written in block diagonal matrix form under an appropriate labeling of the vertices. (b) Show how to label the vertices of the...
(a) Draw the graph corresponding to the 6 7 incidence matrix whose nonzero (/, j) entries equal 1 if j = i and - 1 if j = i + 1, for i = 1 to 6. (b) Find a basis for its kernel and cokemel. (c) How...
Describe, in steps, at least one strategy used to attack embedded operating systems. Describe, in steps, at least one strategy used to defend against the chosen attack.
how does a hypercompetetice environment challenge those in an industry
Describe how managers can reduce unnecessary costs, including real - world examples of how it has been done

Prove that the linear transformation S is invertible. Then find a formula for the inverse linear transformation,

Question:

Step by Step Answer:

First build a matrix representation of S Definition MR We are free to choose whatever bases ...View the full answer

Linear Algebra

Students also viewed these Linear Algebra questions