Q. 4 (a). Determine whether the set is orthogonal and then orthonormal 1 -1 ,0) 五 1 1 -2 ),(- %B (b). Determine whether the mapping T:M,→R is a linear transformation, where, а b = a' +b?

Q: Q2. Let T: R³ R³ be a transformation defined by - ()-() T (a) Is T a linear transformation? Justify…

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Q: Suppose T:R' → R´ is a linear transformation with T(x1, x2, x3) (– 6x1 11x3, 5x2 + 16x3). Find the…

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Q: Prove that S + T and cT are linear transformations.

A: Let S and T are linear transformation then we have to prove that S + T and cT are linear…

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

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Q: Let e₁ = 3 -2 and e₂- Ут and y2= 1 5 8 3 and let T: R² →R² be a [:] = linear transformation that…

A: Step 1: Step 2: Step 3: Step 4:

Q: 6. Let T: R³ → R² be given by 74-7 8-6.5.) = T Show that I is a linear transformation by confirming…

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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: Which of the following is a linear transformation from R2 to R ? a) T(a, b) = (a,0, b²) b) T(a, b) =…

A: Note: As per Bartleby guidelines, for more than 3 parts of a question asked, only 3 has to be…

Q: Let T : P2 → R² be the linear transformation defined by -2а1 + Заз T(a1x² + a2x + a3) = -az + 2az…

A: Explanation of the answer is as follows

Q: ← [:] -[3] = Y₁ 5 into y₁ and maps e2 into y₂. Find the images of Let e₁ = 0 The image of and e₂= 4…

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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: 6. Show that T is a linear transformation. T(x1, x2) = (2x2 – 3x1, x₁ - 4x2, 0, x₂).

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Q: Define the function Q : M2x2 M2x2 by Q(A) = A – AT. Show that Q is a linear transformation. >

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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: T(1,0) =(1,1) T(0,1) = (-1,1)

Q: Q3-B: Verify the Kummer transformation: U(a,c;x) = x¹-U(a-c+1,2-c;x)

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Q: 17. Let T R2 R2 be a linear transformation that maps into - [] into [3]. T is linear to find the…

A: Given: In this question, the given details are, Let T: ℝ2→ℝ2 be a linear transformation that maps.…