Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer. T(X₁X2 X3 X4) = (0,X3

Question

Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer.
T(X₁X2 X3 X4) = (0,X3 +X4X3 X4 X3 X4)
a. Is the linear transformation one-to-one?
1000
OA. T is not one-to-one because the standard matrix A has a free variable.
OB. T is not one-to-one because the columns of the standard matrix A are linearly independent.
OC. T is one-to-one because the column vectors are not scalar multiples of each other.
OD. T is one-to-one because T(x)=0 has only the trivial solution.
b. Is the linear transformation onto?
OA. T is not onto because the first row of the standard matrix A is all zeros.
OB. T is onto because the standard matrix A does not have a pivot position for every row.
OC. T is not onto because the columns of the standard matrix A span Rª
OD. T is onto because the columns of the standard matrix A span R¹

Kunduz · Accepted Answer

Click to see the answer