91Ó°ÊÓ

Determine whether each system of linear equations has (a) one and only one solution, (b) infinitely many solutions, or (c) no solution. Find all solutions whenever they exist. \(\begin{aligned} 2 x-5 y &=10 \\ 6 x-15 y &=30 \end{aligned}\)

Refer to the following matrices: \(A=\left[\begin{array}{rr}-1 & 2 \\ 3 & -2 \\ 4 & 0\end{array}\right] \quad B=\left[\begin{array}{rr}2 & 4 \\ 3 & 1 \\ -2 & 2\end{array}\right]\) \(C=\left[\begin{array}{rrr}3 & -1 & 0 \\ 2 & -2 & 3 \\ 4 & 6 & 2\end{array}\right] \quad D=\left[\begin{array}{rrr}2 & -2 & 4 \\ 3 & 6 & 2 \\\ -2 & 3 & 1\end{array}\right]\) What is the size of \(A ?\) Of \(B\) ? Of \(C\) ? Of \(D\) ?

Find the inverse of the matrix, if it exists. Verify your answer. \(\left[\begin{array}{ll}4 & 2 \\ 6 & 3\end{array}\right]\)

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

Write the system of equations corresponding to each augmented matrix. \(\left[\begin{array}{lll|l}2 & 3 & 1 & 6 \\ 4 & 3 & 2 & 5 \\ 0 & 0 & 0 & 0\end{array}\right]\)

Determine whether each system of linear equations has (a) one and only one solution, (b) infinitely many solutions, or (c) no solution. Find all solutions whenever they exist. \(\begin{aligned} 5 x-6 y &=8 \\ 10 x-12 y &=16 \end{aligned}\)

Refer to the following matrices: \(A=\left[\begin{array}{rr}-1 & 2 \\ 3 & -2 \\ 4 & 0\end{array}\right] \quad B=\left[\begin{array}{rr}2 & 4 \\ 3 & 1 \\ -2 & 2\end{array}\right]\) \(C=\left[\begin{array}{rrr}3 & -1 & 0 \\ 2 & -2 & 3 \\ 4 & 6 & 2\end{array}\right] \quad D=\left[\begin{array}{rrr}2 & -2 & 4 \\ 3 & 6 & 2 \\\ -2 & 3 & 1\end{array}\right]\) Compute \(A+B\).

Determine whether each system of linear equations has (a) one and only one solution, (b) infinitely many solutions, or (c) no solution. Find all solutions whenever they exist. \(\begin{aligned} 4 x-5 y &=14 \\ 2 x+3 y &=-4 \end{aligned}\)

Compute the indicated products. \(\left[\begin{array}{rrr}3 & 1 & 2 \\ -1 & 2 & 4\end{array}\right]\left[\begin{array}{r}4 \\ 1 \\ -2\end{array}\right]\)

Indicate whether the matrix is in rowreduced form. \(\left[\begin{array}{rr|r}1 & 0 & 3 \\ 0 & 1 & -2\end{array}\right]\)