.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:

Which of the following transformations are linear? Select all of the linear transformations. (There may be more than one correct answer) Picture attached

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Give an example (with numbers) to show that the transformation T not linear. Clearly explain why the transformation is not linear. 1. C (o ([2]) 2m = X1 X2 X1X2

The question is attached below . kinldy refer to it

2. Determine whether the mapping T : R4 → R³ defined by X1 2.x1 + 3x4 – 1 X2 T x2 + 5x3 X3 X4 is a linear transformation. Explain your answer.

Which of the following transformations are linear? Select all of the linear transformations. There may be more than one correct answer. Be su you can justify your answers. A. T(A) det(A) from R³x³ to R B. T(A) 1A from R4x3 to R4x3 OC. T(A) = AT from R5x3 to R³x5 1 D. T(A) = A 1 from IR to R2x2 6 8 JE. T(A)= A2 from R4x4 to R4x4 6 5 R.T(A)=[74 -97 A from R2x5 to R2x5

Use the viewing window shown to select a possible equation for the transformation of the parent function. + 8 12 16 20 -8 -12 -16 -20 O y = Vx+5 O y = Vx-5 O y = -Vx-5 O y = -Vx+5 O y = -Vx-6 |

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 X1X2

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) = trace(A) from R³x3 to R OB. T(A) AT from R4x5 to R5x4 0 2 C. T(A) = A [²3] A from R2x2 to R²x2 8 6 OD. T(A) A7 from R6x6 E. T(A) = SAS-1 from R2x2 to R2x2, where S = OF. T(A) det (A) from R5x5 to R to R6x6 -7