Consider a
a. If
b. What can you say about A if
c. If
Learn your wayIncludes step-by-step video
Chapter 3 Solutions
Linear Algebra With Applications (classic Version)
Additional Math Textbook Solutions
College Algebra (10th Edition)
College Algebra with Modeling & Visualization (5th Edition)
Intermediate Algebra (7th Edition)
College Algebra (7th Edition)
Intermediate Algebra for College Students (7th Edition)
- Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).arrow_forwardIn Exercises 7-10, find the standard matrix for the linear transformation T. T(x,y)=(3x+2y,2yx)arrow_forwardLet T:P2P4 be the linear transformation T(p)=x2p. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3,x4}.arrow_forward
- Let T be a linear transformation from R2 into R2 such that T(1,0)=(1,1) and T(0,1)=(1,1). Find T(1,4) and T(2,1).arrow_forwardLet T:P2P3 be the linear transformation T(p)=xp. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3}.arrow_forwardIn Exercises 1-12, determine whether T is a linear transformation. 8. defined byarrow_forward
- In Exercises 1-12, determine whether T is a linear transformation. T:M22M22 defined by T[abcd]=[a+b00c+d]arrow_forwarda Let T=[3001]. What effect does T have on the gray square in Table 1? b Let S=[1002]. What effect does S have on the gray square in Table 1? c Apply S to the vertices of the square, and then apply T to the result. What is the effect of the combined transformation? d Find the product matrix W=TS. e Apply the transformation W to the square. Compare to you final result in part c. What do you notice?arrow_forwardIn Exercises 20-25, find the standard matrix of the given linear transformation from2to 2. Projection onto the line y=2xarrow_forward
- Here is a data matrix for a line drawing: D=[012100002440] aDraw the image represented by D. bLet T=[1101]. Calculate the matrix product TD, and draw the image represented by this product. What is the effect of the transformation T? cExpress T as a product of a shear matrix and a reflection matrix. See Problem 2. 2. Verify that multiplication by the given matrix has the indicated effect when applied to the gray square in the table. Use c=3 in the expansion matrix and c=1 in the shear matrix. T1=[1001] Reflection in yaxis T2=[100c] Expansion or contraction in ydirection T3=[10c1] Shear in ydirectionarrow_forwardIn Exercises 20-25, find the standard matrix of the given linear transformation from ℝ2 to ℝ2. 23. Projection onto the linearrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage