Finding Standard Matrices for Compositions In Exercises
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Chapter 6 Solutions
Elementary Linear Algebra (MindTap Course List)
- Finding Standard Matrices for CompositionsIn Exercises 27-30, find the standard matrices Aand Afor T=T2T1and T=T1T2. T1:R2R2, T1(x,y)=(x2y,2x+3y) T2:R2R2, T2(x,y)=(y,0)arrow_forwardFinding the Standard Matrix and the Image In Exercise 11-22, a find the standard matrix A for the linear transformations T, b use A to find the image of the vector v, and c sketch the graph of v and its image. T is the reflection in the vector w=(3,1) in R2:T(v)=2projwvv, v=(1,4).arrow_forwardFinding the Standard Matrix and the Image In Exercise 11-22, a find the standard matrix A for the linear transformations T, b use A to find the image of the vector v, and c sketch the graph of v and its image. T is the projection onto the vector w=(3,1) in R2:T(v)=2projwv, v=(1,4).arrow_forward
- Coordinate Representation in M3,1 In Exercises 4952, find the coordinate matrix of X relative to the standard basis for M3,1. X=[032]arrow_forwardFinding the Image of a Vector In Exercises 7-10, use the standard matrix for the linear transformation T to find the image of the vector v. T(x1,x2,x3,x4)=(x1x3,x2x4,x3x1,x2+x4), v=(1,2,3,2)arrow_forwardThe determinant of a matrix product In Exercises 1-6, find (a)|A|,(b)|B|,(c)AB and (d)|AB|.Then verify that |A||B|=|AB|. A=[3443],B=[1150]arrow_forward
- Singular Matrices In Exercises 37-42, find the values of ksuch that Ais singular. A=[1k220k314]arrow_forwardShowing That a Function Is an Inner ProductIn Exercises 27 and 28, let A=[a11a12a21a22] and B=[b11b12b21b22] be matrices in the vector space M2,2. Show that the function defines an inner product on M2,2. A,B=2a11b11+a12b12+a21b21+2a22b22arrow_forwardLinear Transformations and Standard Matrices In Exercises 7-18, determine whether the function is a linear transformation. If it is, find its standard matrix A. T:RR2, T(x)=(x,x+2).arrow_forward
- Calculus Let B={1,x,ex,xex} be a basis for a subspace W of the space of continuous functions, and let Dx be the differential operator on W. Find the matrix for Dx relative to the basis B.arrow_forwardFinding the Standard Matrix and the Image In Exercises 11-22, a find the standard matrix A for the linear transformation T, b use A to find the image of the vector v, and c sketch the graph of v and its image. T is the reflection in the y-axis in R2: T(x,y)=(x,y), v=(2,3).arrow_forwardFinding the Standard Matrix and the Image In Exercises 11-22, a find the standard matrix A for the linear transformation T, b use A to find the image of the vector v, and c sketch the graph of v and its image. T is the reflection in the line y=x in R2: T(x,y)=(y,x), v=(3,4).arrow_forward
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