Let L: R2 R³ be a linear mapping such that Find L -19 ([¹2]) -13 absin (a) 8 dr f 8 L D-||| (D-|| = an E

Q: 2(a) A relation R is defined on the set A={1,2,3,4} from A to A, where R' = {(1,2); (1,3); (1,4);…

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Q: 3. f(x, y) = x² x+y + y²-1 -; (1, 1), (-1, 1).

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Q: 3. Find the largest domain (in R2) for the function In(3 + y) 1- x + y f (x, y) :

A: Let's find.

Q: Draw the graph of the function f :R → R defined by f (x) = x3, x∈R.

A: We will make a table for f(x)=x3 x -1 0 1 y -1 0 1

Q: 3. Each of J, K, L, M and N is a linear transformation from R2 to R?. These functions are given as…

A: *part c is asked to solve  Note: To test Injectivity, one simply needs to see if the dimension of…

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Q: Linear transformation T'defined by T(x) = Ax %3D 1 -1 0. where A 1 -2 -3 Determine the Ker(T). 1 1…

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Q: Determine whether the following transformation is linear. Justify you answer. 2x2 T([^])) = [2²²] -…

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Q: Linear transformation T'defined by T(x) = Ax 1 -1 where A 1 -2 -3 Determine the Ran(T). a) Span{ (b)…

A: Given a linear transformation T defined as Tx=Ax, where A=1−101−2−3 We have to determine rangT.…

Q: The mapping L(x) = ax + b is linear. ihi O

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Q: Eliminate the arbitrary constants c₁ and c₂ from the relation y = C₁ + c₂e³x Eliminate the arbitrary…

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Q: Suppose a transformation has a mapping as follows:(x,y)→(1/2 x + 3, -2y + 4). If this mapping were…

A: Given: A function y=x and a transformation mapping x, y→12x+3, -2y+4.

Q: a) Draw y = f(x)] b) Draw y = [f(x)]² 1+ (1, -1) (1, -1) 2 2 (2.5,1) (2.5,1) i) Explain two things…

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Q: Supposer is an invertible function with domain [1, 5] and range [2,7]. Then the domain of r−¹(x − 1)…

A: Given that r is an invertible function with domain [1,5] and range [2,7].It means that for every…

Q: Show that the map t: V,(R) → V3(R) defined by 1(a, b) = (a + b, a- b, b) is a linear transformation.…

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Q: Determine whether the function defined by = 2x1y₁ - x1y2 - x2y1 + 2x2y2 is an inner product on R².

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Q: Find Vf(a), given the following data. Calculate 91, 92 and g3 such that Vƒ(a): 91 92 93 = || || = 91…

A: The given problem is to find the grad f for the given data of directional derivative of function f…

Q: 1 Under the transformation w=-, find the image of y – x + 1 = 0

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Q: Which of the following transformations T: R² → R³ are linear? Find the image of the vector x =…

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Q: Find the value of b so that the point x = (13, b) belongs to the boundary of the set U = {x=R² : x₁…

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Q: Compute f, fy, f fy, and fr of the function. f(x, y)=(2x-3y)* |

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Q: Q-4: Define the mapping T: R³ → R² by T ([] = [ + ] - a) Show that 7' is a linear transformation.…

A: The mapping T:ℝ3→ℝ2 by Txyz=x+yy-z

Q: Let T₁: P₂ → R² and T₂ : R² → R2×2 be linear transformations defined as follows. T₁(ax²+bx+c) = -…

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Q: y y 4 2- 2- -4 -2 2. 4. -4 -2. -2 -2 -4 -4

A: A rectangle and its image

Q: Select the following functions that are bijective. ƒ₂: R → R, ƒ₂(x) = 14 f₂: R → R, f₂(x) = x f₁: R…

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Q: f(x)x| a = __ h=_k= _

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Q: B) IR2 --> IR3           (x, y) --> (x, y2, x+y) Is it linear transformation? investigate.

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Q: (d) Explain why ƒ : 3. Let f: A - B, g : B →C. Do the following. exists, fill in the blanks, and…

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