Finding the Image Two Ways In Exercises
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Chapter 6 Solutions
Elementary Linear Algebra (MindTap Course List)
- Finding the Standard Matrix and the Image In Exercises 23-26, a find the standard matrix A for the linear transformation T and b use A to find the image of the vector v. Use a software program or a graphing utility to verify your result. T(x,y,z)=(2x+3yz,3x2z,2xy+z), v=(1,2,1)arrow_forwardOrthogonal Diagonalization In Exercises 41-46, find a matrix P that orthogonally diagonalizes A. Verify that PTAP gives the correct diagonal form. A=[120210005]arrow_forwardProof Let A be a nonsingular matrix of order 3. Prove that if {v1,v2,v3} is a linearly independent set in M3,1, then the set {Av1,Av2,Av3} is also linearly independent. Explain, by means of an example, why this is not true when A is singular.arrow_forward
- Orthogonal Diagonalization In Exercise 4-52, find a matrix Psuch that PTAPorthogonally diagonalizesAVerify that PTAPgives the correct diagonal form. A=[4200240000420024]arrow_forwardProof Let A be an nn square matrix. Prove that the row vectors of A are linearly dependent if and only if the column vectors of A are linearly dependent.arrow_forwardFinding the Image Two Ways In Exercises 37-42, find T(v)by using (a)the standard matrix and (b)the matrix relative to Band B. T:R2R2, T(x,y)=(3x13y,x4y), v=(4,8), B=B={(2,1),(5,1)}arrow_forward
- Finding the Image Two Ways In Exercises 37-42, find T(v)by using (a)the standard matrix and (b)the matrix relative to Band B. T:R2R3, T(x,y)=(x+y,x,y), v=(5,4), B={(1,1),(0,1)}, B={(1,1,0),(0,1,1),(1,0,1)}arrow_forwardFinding a Coordinate Matrix In Exercises 14, find the coordinate matrix x in Rn relative to the standard basis. x=(5,2)arrow_forwardProof Prove that if A is an nn matrix, then A-AT is skew-symmetric.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning