Find the Standard Matrix of the Linear Transformation T $R ^ { 2 } \rightarrow R ^ { 2 }$

question 7

Multiple Choice

Find the standard matrix of the linear transformation T.
-T: $R ^ { 2 } \rightarrow R ^ { 2 }$ first performs a vertical shear that maps $\mathbf { e } _ { 1 }$ into $\mathbf { e } _ { 1 } + 3 \mathbf { e } _ { 2 }$ , but leaves the vector $\mathbf { e } _ { 2 }$ unchanged, then reflects the result through the horizontal $x _ { 1 }$ -axis.

• A)
• \(\left[ \begin{array} { r r } - 1 & - 3 \\ 0 & 1 \end{array} \right]\)
• B)
• \(\left[ \begin{array} { r r } 1 & 3 \\ 0 & - 1 \end{array} \right]\)
• C)
• \(\left[ \begin{array} { r r } 1 & 0 \\ - 3 & - 1 \end{array} \right]\)
• D)
• \(\left[ \begin{array} { r r } - 1 & 0 \\ 3 & - 1 \end{array} \right]\)

---

Definitions:

Price Ceilings

Government-imposed limits on the prices that can be charged for goods and services to prevent them from becoming too expensive.

Quantity Controls

Government-imposed limits on the quantity of a good that can be produced or sold in the marketplace.

National Football League

The National Football League (NFL) is a professional American football league consisting of 32 teams, divided between the National Football Conference (NFC) and the American Football Conference (AFC).

Licenses

Official permissions granted by authorities allowing individuals or companies to carry out certain activities, such as driving or operating a business.