This question concerns the linear transformation t from Question 3, given by t: R³ R³ (x, y, z) (2x, y + z, z-x), and also the linear transformation s given by S: R³ → P3 (a, b, c)→a-b+ (b+c)x+ (a + c)x². (a) Write down the matrix of s, and find the matrix of sot, in both cases with respect to the standard bases for R³ and P3. (b) Find Kers, and describe it geometrically.

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: Suppose T: R³ → R2 is a linear transformation with T(x1, x2, 3) = (-10x2, -5x1+11x2 - 7x3). Find the…

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Q: 3. Consider the linear transformation T: R R given by T(#1, 12, T3) = (21 + 303,-22- 4x3, 201 +…

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Q: 2. Given the linear transformations: T1:[y1,Y2 ,Y3 ] = [2x1+3x2+X3, 5x1+X3, X2+X3] T2:[Z1,2 ,Z3 ]…

A: The given linear transformations are: T1:y1,y2,y3=2x1+3x2+x3,5x1+x3,x2+x3,T2:z1,z2,z3=y1,y2+y3,y1 a.…

Q: 2. Let T: R³ R³ be the linear transformation given by x1 + x2 + x3 +((:))-[ T X2 2x1 x2 + 7x3 -4x₁ +…

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Q: M = Find the matrix M of the linear transformation T: R³ → R² given by 3 X1 (E)- = X3 T -9x1 - x2 +…

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Q: Find the standard matrix for the linear transformation T: R² 3 and then reflects about the line y…

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Q: Consider a linear transformation T from R³ to R2 Find the matrix A of T. A = for which CD-· -· D-4 0

A: Here for the given transformation we have to find the matrix A of T.

Q: Find a matrix that implements the linear transformation T(x1,x2) = (3x1-4X2, X1-X2, 2x1 + x2)

A: A linear transformation is a function satisfying the following properties: where x and y are…

Q: Let T be the linear transformation defined by T(x, y) = (-2y, 3x + y, 9y - 7x, 5x – 4y). Find its…

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Q: a) Is there exists a linear map T: R² → R² for which T(7,7) = (4,-5) and T(2,2) = (8,-2)? Justify…

A: As per our guidelines, we are supposed to solve only first subpart. Kindly repost other subpart as…

Q: Let T be the linear transformation defined by T(а, у) — (5а + 8y, у, — 4aх — 2у, — 6ӕ — Зу). Find…

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Q: Define a linear transformation T : R? → R37: R - R' by T(a1, x2) = (3xı + a2, 5a1 + 7x2, 2a1 + 3x2)…

A: Given linear transformation t :ℝ2→ℝ3  deined by Tx1, x2 =3x1, x2+5x1, 7x2+2x1, 3x2.we have to find a…

Q: Consider the transformation T(1, 2, 3) = (2x1 - x2 + x3, x2 + x3,0). (a) Form the standard matrix A…

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Q: Find the standard matrix of the given linear transformation from R2 to R2 Projection onto the line y…

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Q: Find (a) the image of and (b) the preimage of for the linear transformation. T: R³ → R³, T(v, V2,…

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Q: Consider the linear map T : R² → R² which sends (1,0) → (-3, 5) and (0, 1) → (4, –1). (a) What is…

A: Follow step 2.

Q: M = Find the matrix M of the linear transformation T: R³ → R² given by * ((:D) - T = 2x1x₂ + (-7):…

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Q: M = Find the matrix M of the linear transformation T: R³ →>> X1 X2 X3 = R² given by [90]. -6x1 - x2…

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Q: Write down the matrix A that represents the linear transformation ƒ : R² - (a) R² (i.e. so that f(x)…

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Q: 6. Let T be a linear transformation from R to R?given by T(x, x2x3) = (3x1 - 5x2 + X3, X1 + 6X3)…

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Q: (3)The region between 4=5 and y=x+ 4 is rotated about x=-\. Uge cylindrical shells to find the…

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Q: Determine the matrix of the linear transformation T(x, y) = (3x + 5y, 3y – 2x) 5 -2 3 (a) -2 3 (b)…

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Q: Find the matrix of the linear transformation T from R? R?, where T([1, 0]) = [1, -2], and T([2, 1])…

A: Given linear transformation T:R2→R2 Where, T1,0=1,−2 and T2,1=2,3 We have to find the matrix…

Q: Find the matrix of the linear transformation T from R2 -> R² where T([1, 0]) = [1, –2] and T([2, 1)…

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Q: Suppose T is a linear transformation on R² (i.e. T(x, y) = (ax + by, cx + dy) where a, b, c, d are…

A: Linear transformation

Q: 3.T(x, y, z) = (x+y, x − y, z− x) Answer 4. T (x, y) = (5x + y, 0, 4x - 5y) 5. T (x, y, z) = (3x −…

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