Problem 1

In Exercises \(1-10\), show that \(B\) is the inverse of \(A\). $$ A=\left[\begin{array}{ll} 7 & 4 \\ 5 & 3 \end{array}\right], B=\left[\begin{array}{rr} 3 & -4 \\ -5 & 7 \end{array}\right] $$

Problem 1

In Exercises \(1-16\) find the determinant of the matrix. $$ [-5] $$

Problem 1

Determine the dimension of the matrix. $$ \left[\begin{array}{rrr} 0 & -3 & 0 \\ 9 & 2 & -7 \end{array}\right] $$

Problem 1

Find \(x\) and \(y\). $$ \left[\begin{array}{rr} 4 & x \\ -1 & y \end{array}\right]=\left[\begin{array}{rr} 4 & -3 \\ -1 & 2 \end{array}\right] $$

Problem 2

Show that \(B\) is the inverse of \(A\). $$ A=\left[\begin{array}{ll} -4 & 1 \\ -9 & 2 \end{array}\right], B=\left[\begin{array}{ll} 2 & -1 \\ 9 & -4 \end{array}\right] $$

Problem 2

Find \(x\) and \(y\). $$ \left[\begin{array}{rr} x & -7 \\ 9 & y \end{array}\right]=\left[\begin{array}{ll} 5 & -7 \\ 9 & -8 \end{array}\right] $$

Problem 2

Find the determinant of the matrix. $$ [6] $$

Problem 2

Determine the dimension of the matrix. $$ \left[\begin{array}{lll} -7 & 21 \end{array}\right] $$

Problem 3

Determine the dimension of the matrix. $$ \left[\begin{array}{lll} 6 & 4 & 1 \\ 8 & 3 & 0 \\ -1 & 2 & 1 \\ 1 & 5 & 4 \end{array}\right] $$

Problem 3

Show that \(B\) is the inverse of \(A\). $$ A=\left[\begin{array}{ll} 2 & -1 \\ 5 & -4 \end{array}\right], B=\left[\begin{array}{rr} \frac{4}{3} & -\frac{1}{3} \\ \frac{5}{3} & -\frac{2}{3} \end{array}\right] $$