\( 0: 32 \) II \( \leq \) (B)
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Question 4
Suppose that a garden supply store sells three mixtures of grass seed. The deluxe mixture is \( 60 \% \) bermudagrass \( 40 \% \) bluegrass and \( 0 \% \) rye, the standard mixture is \( 40 \% \) bermudagrass \( 60 \% \) bluegrass and \( 0 \% \) rye, and the economy mixture is \( 20 \% \) bermudagrass \( 20 \% \) bluegrass and \( 60 \% \) rye.
A customer wants to purchase a blend (mixture) of grass seed containing \( 3 \mathrm{~kg} \) of bermudagrass, \( 3 \mathrm{~kg} \) bluegrass and \( 3 \mathrm{~kg} \) of rye; ( 25 points total)
a. Is it possible to combine the three mixtures of seed into a blend that has exactly the desired amounts of bermudagrass, bluegrass and rye, with no surplus of either? If yes, which formula the store clerk should use? (10 points)
b. How much of each mixture should the store clerk add to the blend to fulfill the customer's above request? (15 points)
\( 4 / 5 \)
Question 5 Assume that \( T \) is a linear transformation such that \( T: R^{2} \rightarrow R^{4}, T\left(e_{1}\right)=\left[\begin{array}{l}3 \\ 1 \\ 3 \\ 1\end{array}\right] \), \( T\left(e_{2}\right)=\left[\begin{array}{r}-5 \\ 2 \\ 0 \\ 0\end{array}\right] ;(15 \) points total \( ) \)
a. Find the standard matrix of \( T \), (7 points)
b. Determine if the linear transformation is one-to-one, or onto or both. (8 points)
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