Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer.T(X?X2...

90.2K

Verified Solution

Question

Calculus

Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer.T(X?X2 X3 X4) = (0,X3 +X4X3 X4 X3 X4)a. Is the linear transformation one-to-one?1000OA. 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 ROD. T is onto because the columns of the standard matrix A span R

Answer & Explanation Solved by verified expert

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member

Transcribed Image Text

Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify your answer.T(X?X2 X3 X4) = (0,X3 +X4X3 X4 X3 X4)a. Is the linear transformation one-to-one?1000OA. 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 ROD. T is onto because the columns of the standard matrix A span R