In Exercises 13-16, use a rectangular
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- Q.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_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-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
- Determine 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_forwardLet A = [1 -1 -1 -1 1 -1 -1 -1 1]. Find a diagonalization if possible.arrow_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_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 (1) is linear and isometry. c. Draw the vectors x and R (I) forx:arrow_forwardFind the metrix of given linear transformationarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage