If T:P1→P1 is a linear transformation such that T(1+4x)=−1+2x and T(5+19x)=4−2x, then T(−2−4x)=
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If T:P1→P1 is a linear transformation such that T(1+4x)=−1+2x and T(5+19x)=4−2x, then
T(−2−4x)=
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- Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).Let T be a linear transformation from R³ into R³. Find T-1 T(x1x₂x3) = (2x1-X3, X₁ + X₂ X3, X2-3X3) T(X₁₁X₁₁X3) = (2x₁+x₂ −X3, −3x₁+6x₂−x3, −X₁+2×₂-2x3) b. T(x1x2x3) = (2x₁ + x₂ -2X3, X₂-X3, X1 + X3) c. T(x₁,x₂₁x3) = (2x₁ + x₂ -2X3, X₂-X3, -X₁ + X3) d. T(x1,x2x3) = (4x₁-2×₂-X3, X₁-X₂, −3x₁+2x₂ + x3) T(X₁, X₂2₁×3) = (-x₁ + 3x₂ + 3x3, −3x₁-x₂ + 4x3,2x₁ − ×2 −X3) a. e.Which of the following transformations are linear? Yı=x3 A. Y2=13 Y3=x1 Yı=8x2 O B. Y2=-6x3 Y3=-3x1 Y1=-9x1 Y2=7x1 Y3=6x1 С. Y1=x1 + 5 D. Y2=x2 Y1=0 E. Y2=X1X2 Y1=4x1+ x2 O F. 42=-x1
- Find the inverse of the linear transformation x1 = x2 = x3 = Y1+ Y₁+ Y1+ Y1 Y2 Y3 = = = 4x1 5x1 x1 -8x2 -29x3 -11x2 -38x3 - 2x2 -7x3 Y2+ Y2+ Y2+ Y3, Y3₁ Y3.Show that the transformation T defined by T(x1, X2) = (2x,- 3x,, x1 +4, 5x,) is not linear. %3DLet T be a linear transformation from P₂ into P₂ such that T(1) = x, T(x) = 1 + x, and 7(x2) = 1 + x + x². Find 7(1 - 7x + 2x²). T(1 - 7x + 2x²) = Need Help? Read It Need Help? Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function. (Use C for the constant of integration.) Dx(f) = 8x + 6 Watch It Read It
- Let T be a linear transformation from P₂ into P₂ such that T(1) = x, T(x) = 1 + x, and T(x²) = 1 + x + x². Find 7(2 − 8x + x²). T(2 8x + x²) =Let T be a linear transformation from P2 T(2 - 7x + x²) = into P₂ such that T(1) = x, 7(x) = 1 + x, and 7(x²) = 1 + x + x². Find 7(2 - 7x + x²).Write the matrix corresponding to the following linear transformations. Yı 2x1 – x2 – x3 Y2 3x3 Y3 = x1 + x2 2. -1 -1 3 1 1 2 -1 -1 3 1 2 -1 -1 1 1 1 2. -1 1 3 1 1 1
- 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.. Let T be a linear transformation induced by the matrix A = 4 2 - 3 -2 . Find the matrix of T-¹.If T: P₁ → P₁ is a linear transformation such that T(1+4x)= -2 + 4x and T(4+15x) = - 3 - 4x, then T(1-2x) =