In Exercises 13-16, use a rectangular
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- Show that T is a linear transformationarrow_forwardQ.2. a. Find the transformation R (x) which reflect each vector x= through the 1 the vector u = b. Show that the transformation R (x)is linear and isometry.arrow_forward-2 Use a rectangular coordinate system to plot u = ,v = 1, and their images under the 4 -1 given transformation T(x) = | Describe geometrically what T does to each vector in R2.arrow_forward
- Let A = [1 -1 -1 -1 1 -1 -1 -1 1]. Find a diagonalization if possible.arrow_forwardReduce the given quadratic form to canonical form by an orthogonal transformation.arrow_forwardDetermine if the specified linear transformation is (a) one-to-one and (b) onto. Justify each answer. T(X1 X2 X3) = (x₁ - 4x2 +6x3, X2-9x3) (a) Is the linear transformation one-to-one? O A. T is one-to-one because the column vectors are not scalar multiples of each other. B. T is one-to-one because T(x) = 0 has only the trivial solution. O C. T is not one-to-one because the columns of the standard matrix A are linearly independent. O D. T is not one-to-one because the columns of the standard matrix A are linearly dependent.arrow_forward
- find the vector projection of x into √xarrow_forwardQ.2. a. Find the transformation R, (x) which reflect each vector x = through the line along the vector u = b. Show that the transformation R, (x) is linear and isometry. c. Draw the vectors x and R, (x) for x=|arrow_forwardFind the metrix of given linear transformationarrow_forward
- Use a rectangular coordinate system to plot u = and their images under the given transformation T. Describe geometrically what T does to each vector x in R2. x1 -1 T(x) = 0 -1 X2 Which graph below shows and its image under the given transformation? O A. OB. Oc. OD. Which graph below shows v and its image under the given transformation? OA. OB. OC. OD. What does T do geometrically to each vector x in R2? O A. A projection onto the x,-axis O B. A reflection through the origin OC. A dilation transformation over the x,-axis O D. A shear transformationarrow_forwardIn Exercises 13-16, use a rectangular coordinate system to plot 5 = [2] - [ - ] V = 4 (Make a separate and reasonably large sketch for each exercise.) Describe geometrically what T does to each vector x in R². u= and their images under the given transformation T.arrow_forwardIn Exercises 13-16, use a rectangular coordinate system to plot 5 -2 -[2], V u= V = , and their images under the given transformation T. 4 (Make a separate and reasonably large sketch for each exercise.) Describe geometrically what I does to each vector x in R².arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage