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Differential Equations and Linear Algebra (4th Edition)
- Which of the following transformations are linear? DA. T(A) = A + I3 from R³x3 to R³×³ OB. T(A)=9A from R6x4 to R6x4 OC. T(A) = A² from R6x6 to R6x6 5 D. T(4) = [4 34 A from R2x3 to R2x3 E.T(A) SAS-¹ OF. T(A) = AT from = from R²x2 to R²x2, where S= R³x4 to R4x3 -5arrow_forward.Define f: R- R by f(x) = rx + d, where r and d are real constants. Show that for f to be linear, it is required that d 0. (the definition of a linear transformation is given in text section 1.8) ()- 4r1-2 . Is the transformation T linear? YES or NO (circle one) I2 X122+3 Justify your answer:arrow_forwardWhich of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. A. T(A) = AT from R 5x4 to R 4x5 B. T(A) = A7 from R 3x3 to R 3x3 C. T(A) = 9A from R 3x4 to R 3x4 D. T(A) = SAS-¹ from R 2x2 to R 2x2, where S = 0 E. T(A) = ASA-¹ from R 2x2 to R 2x2, where S = 8 DET(A) = [ 32 ] F. A from R 2x5 to R2x5 6 -8 0 B -3 9 2 -4arrow_forward
- 18. Apply the transformation Ax for the following: 3 A = 2 -1 X = -4 Then, plot x and Ax.arrow_forward7. Consider the transformation w = 5x1- 3r, w =2x1+x2. Detemine whether the transformation is one-to-one.arrow_forwardWhich of the following transformations are linear? Check all that apply. Note you only have 5 attempts. (E]). [4x - 5y + 2z 9y - 7z = -10x - 3y -2x 5x 8x [6x] A. T B. T C. T OD. T ([]) ¹ ([₁]) = x E. T ([]) F. T = = (1) (1) = = [7x + -X 7 30 10 [y²] N X '5arrow_forward
- For each question below, T: R" → R" where n = 2 or 3 such that T(x) = y. Which of the following transformations are linear? UA. B. C. OD. E. OF. Y1 Y2 Y1 Y2 Y1 Y2 Y1 Y2 Y3 Y1 = = = = Y2 Y1 Y2 = = 0 5x2 7x1 9 2x1 + x2 -X1 -3x1 4x1 6x1 x1 +8 X2 0 X1X2arrow_forwardLet T be a linear transformation from P₂ into P₂ such that T(1) = x, T(x) = 1 + x, and T(x²) = 1 + x + x². Find 7(2 − 8x + x²). T(2 8x + x²) =arrow_forward4. Describe the transformations of y=-2f[3(x– 4)]–5.arrow_forward
- Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be sure you can justify your answers. □A. T(A) = AT from R4x6 to R6x4 B. T(A) = det(A) from R6×6 to R C. T(A) 4A from R5X6 to R5x6 D. T(A) = A -4 7 = 3 6 E. T(A) = A³ from R5X5 = A[2₁ F. T(A) = A from R to R²x2 to R 5x5 9 -8 3 1-[2 9 8 1 A from R2x2 to R2x2arrow_forwardWhich of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. OD. T(A) = det(A) from R6×6 OE. T(A) = A² from Rt> to R 4×4 to R4×4 F. T(A) = SAS 3 to R2x2, where S = 1 7 from R2×2 -1arrow_forwardIfT: R³ R³ is a linear transformation such that 2 () 5 then T 040804 = -4 T = 1 T T -2 = -2arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning