Let T: R2 → P₂ be a linear transformation for which :) ----²-------² = = 12x and T = + = + Find T and 2 We will first fi

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Let T R2 P Be A Linear Transformation For Which 12x And T Find T And 2 We Will First Fi 1 (111.33 KiB) Viewed 24 times

Let T R2 P Be A Linear Transformation For Which 12x And T Find T And 2 We Will First Fi 2 (133.4 KiB) Viewed 24 times

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Let T: R2 → P₂ be a linear transformation for which ----²-------² = = 12x and T = + = + Find T and 2 We will first find T [9] √ [1] == nd [3] = x + 2x2, noting that T is a linear transformation from R2 to P₂. A basis B for R2 is as follows. - (1) (²) [:] we first express this vector as a linear combination of the basis elements. In other 9 We know the result of the transformation T on the elements of the basis. Therefore, to find T words, we need to find c₁ and c₂ such that the following is true. =4[1] C1 + €₂ -1 Step 1 B = given that T = 1 - 2x and T
To solve for c₁ and c₂, set up a system of equations. 0 1 2 8-8+4) = C₂ 9 1 ] x ) ²₂ = 0 C₁ - C₂ = Solve for and C₂ C1 C1 C2 =