Finding the Standard Matrix and the Image In Exercise
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Chapter 6 Solutions
Elementary Linear Algebra (MindTap Course List)
- Find a basis for R2 that includes the vector (2,2).arrow_forwardFind an orthogonal matrix P such that PTAP diagonalizes the symmetric matrix A=[1331].arrow_forwardUse the standard matrix for counterclockwise rotation in R2 to rotate the triangle with vertices (3,5), (5,3) and (3,0) counterclockwise 90 about the origin. Graph the triangles.arrow_forward
- 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_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_forwardFind the determinant of the matrix in Exercise 15 using the method of expansion by cofactors. Use a the second row and b the second column. 15. [321456231]arrow_forward
- Rotate the triangle in Exercise 29 counterclockwise 90 about the point (5,3). Graph the triangles. 29. Use the standard matrix for counterclockwise rotation in R2 to rotate the triangle with vertices (3,5), (5,3) and (3,0) counterclockwise 90 about the origin. Graph the triangles.arrow_forward(3) Find the matrix of the linear transformation that sends a vector to its reflection to the plane x1 – x2 + x3 = 0.arrow_forwardLet T be the linear transformation associated with the matrix: 0 1 -1 0 Find T(V) if V is the vector: 2 2 Is the transformation a rotation or a reflection? Justify why.arrow_forward
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