Search problems

4 problems match “determinants”. Clear

Visitors search a sample. Sign in for free to search every problem. Sign in

1. Area of a triangle from vectors ●○○○○ 10 ptsLet $\mathbf{a} = \begin{pmatrix} 5 \\ 1 \end{pmatrix}$ and $\mathbf{b} = \begin{pmatrix} 2 \\ 4 \end{pmatrix}$. Find the area of the triangle with vertices $\mathbf{0}$, $\mathbf{a}$, and $\mathbf{b}$.
2. Value of x making a matrix singular ●○○○○ 10 ptsFind the value of $x$ for which the matrix $\begin{pmatrix} 1 + x & 7 \\ 3 - x & 8 \end{pmatrix}$ is not invertible. Round to two decimal places.
3. Singular 2x2 matrix parameter ●○○○○ 10 ptsFor which values of $\lambda$ does $A^{-1}$ not exist, where $A=\begin{pmatrix}\lambda&1\\-1&-\lambda\end{pmatrix}$? Give all such values in increasing order.
4. Cross product of two vectors ●○○○○ 10 ptsFind $(2\hat{i}+3\hat{j}-\hat{k})\times(3\hat{j}+2\hat{k})$. Write the result as $a\hat{i}+b\hat{j}+c\hat{k}$ and enter the coefficients $a$, $b$, $c$.