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_forwardVector Transformations with Matricesarrow_forwardThe linear transformation T: R R rotates points about the origin through - radians and then reflects through the horizontal z, axis. In this case, the standard matrix of T isarrow_forward
- (a) Find a rotation matrix that maps the vector v= (1,1,1) into (1,-1,1) . (b) Find a rotation matrix that maps the vector v= (0,V3/2,-1/2) into (-1,0,0>arrow_forwardthe range Find the standard matrix of a linear transformation T:R³ →R² such that [] 27 of T is spanned by the vectors andarrow_forward(1 point) The matrices - [8]. [J]. - [8] ·^ - [i]· A4 = A₁ = A3 = , A₂ = form a basis for the linear space V = R2X2. Write the matrix of the linear transformation T: R2x2 relative to this basis. R2x2 such that T(A) = 4A + 15ATarrow_forward
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