Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer. T(*1,x2,X3,44) = (

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Determine If The Specified Linear Transformation Is A One To One And B Onto Justify Your Answer T 1 X2 X3 44 1 (50.68 KiB) Viewed 20 times

Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer. T(*1,x2,X3,44) = (0,X, + X3,xy + x>.x2 + x3) a. Is the linear transformation one-to-one? U O A. Tis not one-to-one because the standard matrix A has a free variable. B. Tis one-to-one because T(x) = 0 has only the trivial solution. O C. T is not one-to-one because the columns of the standard matrix A are linearly independent. OD. Tis one-to-one because the column vectors are not scalar multiples of each other. U br b. Is the linear transformation onto? le je he O A. Tis onto because the standard matrix A does not have a pivot position for every row. OB. Tis not onto because the columns of the standard matrix A span Rº. OC. T is not onto because the first row of the standard matrix A is all zeros, OD. Tis onto because the columns of the standard matrix A span R". Бе