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- Let T be a linear transformation from R2 into R2 such that T(4,2)=(2,2) and T(3,3)=(3,3). Find T(7,2).Find nullity of linear transformation T(x1,x2,x3)=(x1-x2,x1+x3)Evaluate SR(3x+6y)dA where R is the triangle with vertices (0,3), (4,1), and (2,6) using the transformation x=글 (u-v) y=}(3u+v+12) Please make sure to draw a sketch for of R in terms of xy and uv. And be clear to state the Jacobian for the transformation.
- B) IR2 --> IR3 (x, y) --> (x, y2, x+y) Is it linear transformation? investigate.Define linear transformations S : P1 ---> P2 and T: P2---> P1 by S(a + bx) = a + (a + b )x + 2bx2 and T ( a + bx + cx2) = b + 2cx Compute (S 0 T)(3 + 2x - x2) and (S 0 T)(a + bx + cx2). Can you compute ( T 0 S) (a + bx) ? If so, compute it.Suppose that a linear transformation T satisfies 5 1 T(u,) = -1 T(u,) = 1 -2 Find T(4u, - 3u,). T(4u, - 3u,) =
- Define the linear transformation T by T(x) = Ax. Find ker(T), nullity(T), range(T), and rank(T). 0 -8 2 A 16 0 19 (а) ker(T) (If there are an infinite number of solutions uset as your parameter.) } 16 1 t, -t,t 19 4Find a linear transformation T : P2 → P3 such that T(x^2) = x^3, T(x + 1) = 0, T(x − 1) = x.Also, compute T(v) when v = x^2 + x + 1.(x- a2+b2 2b (ax + by + c) 2a (ах + by + c), у — a²+b2 2. Verify that the mapping (x, y) → is a transformation.