Solve the Problem Determine Whether the Linear Transformation $\mathrm { T }$

question 63

Multiple Choice

Solve the problem.
- $$\mathrm { T } \left( \mathrm { x } _ { 1 } , \mathrm { x } _ { 2 } , \mathrm { x } _ { 3 } \right) = \left( - 4 \mathrm { x } _ { 2 } - 4 \mathrm { x } _ { 3 } , - 2 \mathrm { x } _ { 1 } + 8 \mathrm { x } _ { 2 } + 4 \mathrm { x } _ { 3 } , - \mathrm { x } _ { 1 } - 2 \mathrm { x } _ { 3 } , 4 \mathrm { x } _ { 2 } + 4 \mathrm { x } _ { 3 } \right)$$
Determine whether the linear transformation $\mathrm { T }$ is one-to-one and whether it maps $\mathfrak { R } ^ { 3 }$ onto $\mathfrak { R } ^ { 4 }$ .

• A) One-to-one; not onto \(R ^ { 4 }\)
• B) Not one-to-one; onto \(R 24\)
• C) Not one-to-one; not onto \(R ^ { 4 }\)
• D) One-to-one; onto \(R ^ { 4 }\)

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