Let S: R²- → R² and T: R² → R² be linear transformations such that 4 As = [2²] and AS-T = [3/2 3/2] where S T is the composition of S and T. Then T is the function whose matrix AT is given by [2√3/2 3/2 1 ° [3³/2 J 3 3/2 3 3/2 " 4 [123] ° [21][3/2 3/2] There are infinitely many possible functions T.

Q: Find x such that T(x) = (7,12).

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Q: Determine whether the given transformation is linear or not? T(x, X2, X3) = (X1,X2, XzX3)

A: Any transformation T is linear if and only if (a) T(x+y) = T(x)+T(y) (b) T(ax) = aT(x) Given Tx1 ,…

Q: Let f:  V-->W be any linear transformation. What are possible solutions to f(0)?

A: Note: A Linear Transformation Maps the Zero vector to the Zero Vector.

Q: Let T: R² R² be a linear transformation that sends the vector u = (5,2) into (2, 1) and maps v = (1,…

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Q: 4. Let T: R" → Rm be a linear transformation and suppose T(u) = v. Show that T(-u) = -v.

A: Since T is a linear transformation, for any scalar number c, we must have,        T(cu) = cT(u)

Q: Is b in the range of the linear transformation X-Ax? Why or why not? A = 2 -4 1 -6 7 5 3-1 b -1 6

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Q: If U:M3x2(F)-->F6 is a linear transformation, then U is an isomorphism.

A: True.

Q: Let T : R? → R² and T2 : R? → R² be linear transformations defined as follows. (:) - ax2 T1 bæ1 T2…

A: We find composition of two Linear transformation

Q: Is this function f a linear transformation?

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Q: Let T:R" R" be a linear transformation, and let {V1, V2, V3} be a linearly dependent set in R".…

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Q: Let T1 : P2 → R² and T2 : R? → R2x2 be linear transformations defined as follows. a + b b - T1(ax? +…

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Q: Determine whether the following transformation from R3 to R² is linear.

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Q: Let T1 : R? → R² and T2 : R? → R? be linear transformations defined as follows. -2x1 T: (:) -L -5x1…

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Q: Let T be a linear transformation from R2 into R2 such that  T(1, 0) = (1, 1)  and  T(0, 1) = (−1,…

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Q: Let T be a linear transformation from R2 into R2 such that T(1, 0) = (1, 1) and T(0, 1) = (-1, 1).…

A: Given: T:R2→R2 To find: T8,1,T-5,1

Q: Let T: R? » P2(R) and U : R' → M2x2 (R) be lincar transformations. A student claims U must be…

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Q: b = TT and let A = 3 2 1 0 1 4 0 1 00:00

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Q: Let T be a linear transformation from P₂ into P₂ such that 7(1) = x, T(x) = 1 + x, and 7(x2) = 1 + x…

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Q: T₁ State University, 202 I1 I2 yright Texas State University, 2023. All rights reserved. 2x11₂ a.…

A: Given: Let T1 and T2 be the linear transformations defined by T1: x1x2→2x1-x24x1 , T2:…

Q: Let D, be the linear transformation from C'la, b] into Cla, b] from this example. Determine whether…

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Q: Let T : R? → R² and T, : R? → R² be linear transformations defined as follows. (:)-L- X1 3x1 T1 x2…

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Q: ppose that T : R² → R² is a linear transformation and that 7([일) -B] T and ar (H) nd T

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Q: find a linear transformation that T:R2 -> R3 T(1, 2) = (1, -1, 2) T(1, 3) = (3, 0, 1) T(1, 1) =…

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Q: Select one or more: O a. The function R → R’ which maps a number x to the vector ū = (x, 2x, x²) O…

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Q: Let T: R2→R? be a linear transformation such that T (x,X2) = (X1 +x2, 4x, +3x2) . Find x such that…

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Q: Let D, be the linear transformation from C'[a, b] into C[a, b] from this example. Determine whether…

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Q: Show that projw is a linear transformation and that (projw)² = projw.

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Q: Let T: R² R² be a linear transformation that maps u= to find the image of 2u + v. O A. O B. O C. O…

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Q: Suppose that T is a linear transformation, with T(u,) = T(u2) =:: Find T(2u, - 3u,).

A: From the definition of linear transformation we can solve this question.