Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify each answer. T(X1.X2.X3) = (X1 - 5x2 + 5X3, X2 = 9X3) (a) Is the linear transformation one-to-one? O A. Tis not one-to-one because the columns of the standard matrix A are linearly independent. O B. Tis one-to-one because T(x) = 0 has only the trivial solution. O C. Tis not one-to-one because the columns of the standard matrix A are linearly dependent. O D. Tis one-to-one because the column vectors are not scalar multiples of each other. (b) Is the linear transformation onto? O A. Tis not onto because the columns of the standard matrix A span R2. B. Tis onto because the standard matrix A does not have a pivot position for every row. С. Tis onto because the columns of the standard matrix A span R. O D. Tis not onto because the standard matrix A does not have a pivot position for every row.

find A³. Write A³ input your answer below: a11 = a12 = 921 = Given the matrix 922 || 0 -3 [83]. -3 A = = A³ = - a11 a21 a12 922

QI. Write the following models using matrix notation, Y = XB +e : (a) Multiple regression, Y = Bo +BXin + B2xi2 + B3X13 + ei; i=1, 2, 3, ..., 7. (b) Multiple polynomial regression, Y; = Bo + Bxi1 + B2Xi2 + B3x + B4x + B5X11X12 + ei; i= 1, 2, 3, ..., 7 (c) Two-way ANCOVA with no interaction and common slope, Yi = µ+a; + Bj + yxijk + ei; i=1, 2, 3; j= 1, 2; k= 1, 2.

Write a function for the blue graph of a quadratic function in a form: f(x) = a (b (x + c))2 + d (1, 1). (0,0) 2 (0, –1) (-1, –3)