Indicate whether the matrix is in rowreduced form. \(\left[\begin{array}{ll|l}1 & 1 & 3 \\ 0 & 0 & 0\end{array}\right]\)

Lawnco produces three grades of commercial fertilizers. A \(100-\mathrm{lb}\) bag of grade \(\mathrm{A}\) fertilizer contains \(18 \mathrm{lb}\) of nitrogen, $4 \mathrm{lb}\( of phosphate, and \)5 \mathrm{lb}$ of potassium. A \(100-\mathrm{lb}\) bag of grade \(\mathrm{B}\) fertilizer contains $20 \mathrm{lb}\( of nitrogen and \)4 \mathrm{lb}$ each of phosphate and potassium. A 100-lb bag of grade \(\mathrm{C}\) fertilizer contains \(24 \mathrm{lb}\) of nitrogen, \(3 \mathrm{lb}\) of phosphate, and \(6 \mathrm{lb}\) of potassium. How many 100 -lb bags of each of the three grades of fertilizers should Lawnco produce if a. \(26,400 \mathrm{lb}\) of nitrogen, \(4900 \mathrm{lb}\) of phosphate, and \(6200 \mathrm{lb}\) of potassium are available and all the nutrients are used? b. \(21,800 \mathrm{lb}\) of nitrogen, \(4200 \mathrm{lb}\) of phosphate, and \(5300 \mathrm{lb}\) of potassium are available and all the nutrients are used?

(a) write each system of equations as a matrix equation and (b) solve the system of equations by using the inverse of the coefficient matrix. \(\quad x+2 y=b_{1}$$2 x-y=b_{2}\) where (i) \(b_{1}=14, b_{2}=5\) and (ii) \(b_{1}=4, b_{2}=-1\)

Let $$A=\left[\begin{array}{rr}2 & 2 \\\\-2 & -2\end{array}\right]$$ Show that \(A^{2}=0\). Compare this with the equation \(a^{2}=0\), where \(a\) is a real number.

Compute the indicated products. $\left[\begin{array}{rr}-1 & 3 \\ 5 & 0\end{array}\right]\left[\begin{array}{l}7 \\ 2\end{array}\right]$

Compute the indicated products. $\left[\begin{array}{rrr}6 & -3 & 0 \\ -2 & 1 & -8 \\ 4 & -4 & 9\end{array}\right]\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$