-Suppose $B = \left\{ b _ { 1 } , b _ { 2 } , b _ { 3 } \right\}$

question 10

Multiple Choice

$$\text { Find the matrix of the linear transformation } \mathrm { T } : \mathrm { V } \rightarrow \mathrm { W } \text { relative to } \mathrm { B } \text { and } \mathrm { C } \text {. }$$
-Suppose $B = \left\{ b _ { 1 } , b _ { 2 } , b _ { 3 } \right\}$ is a basis for $V$ and $C = \left\{ c _ { 1 } , c _ { 2 } \right\}$ is a basis for $W$ . Let $T$ be defined by
$$\begin{array} { l } \mathrm { T } \left( \mathbf { b } _ { 1 } \right) = 3 \mathbf { c } _ { 1 } + \mathrm { c } _ { 2 } \\\mathrm {~T} \left( \mathbf { b } _ { 2 } \right) = 8 \mathbf { c } _ { 1 } - 8 \mathbf { c } _ { 2 } \\\mathrm {~T} \left( \mathbf { b } _ { 3 } \right) = 3 \mathbf { c } _ { 1 } + 2 \mathbf { c } _ { 2 }\end{array}$$

• A)
• \(\left[ \begin{array} { r r r } 4 & 0 & 5 \\ 1 & - 8 & 2 \end{array} \right]\)
• B)
• \(\left[ \begin{array} { r r r } 3 & 8 & 3 \\ 1 & - 8 & 2 \end{array} \right]\)
• C)
• \(\left[ \begin{array} { r r } 3 & 1 \\ 8 & - 8 \\ 3 & 2 \end{array} \right]\)
• D)
• \(\left[ \begin{array} { l l } 3 & 4 \\ 8 & 0 \\ 3 & 5 \end{array} \right]\)

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Definitions:

Intravenous Antibiotic

Antibiotic medication administered directly into the bloodstream through an IV to treat infections.

Severe Diarrhea

An intense or acute condition characterized by the frequent passage of loose, water stools that can lead to dehydration.

Contact Precautions

Measures taken in healthcare settings to prevent the spread of infections through direct or indirect contact with patients or their environment.

Airborne Precautions

Infection control measures taken to prevent disease transmission through air currents, relevant for pathogens that can travel on dust particles or small respiratory droplets.