Try the fastest way to create flashcards
Question

# Evaluate each determinant.$\left| \begin{array} { r r r } { 2 } & { 0 } & { \frac { 1 } { 2 } } \\ { 1 } & { 0 } & { 2 } \\ { 4 } & { 0 } & { - 5 } \end{array} \right|$

Solution

Verified
Step 1
1 of 2

$\text{\color{#c34632}Consider a n\times n matrix such that n\geq3: (1) You can select any row or column to expand its determinant. (2) Once the row/column is selected, multiply each element of that row/column by its cofactor, then add all these products. (3) The sum-product described above is equal to the determinant of the original matrix. }$

Let us expand this determinant along column 2 because it has the maximum zeros.

$\left|\begin{array}{ccc} 2 & 0 & \dfrac{1}{2}\\\\ 1 & 0 & 2 \\\\ 4 & 0 & -5\end{array}\right|=0\cdot \left(-1\right)^{1+2}\cdot\left|\begin{array}{cc} 1 & 2 \\ 4 & -5\end{array}\right|+0\cdot \left(-1\right)^{2+2}\cdot \left|\begin{array}{cc} 2 & \dfrac{1}{2} \\\\ 4 & -5\end{array}\right|+0\cdot \left(-1\right)^{3+2}\cdot \left|\begin{array}{cc} 2 & \dfrac{1}{2}\\\\ 1 & 2 \end{array}\right|$

$=0+0+0=0$

## Recommended textbook solutions

#### Precalculus

2nd EditionISBN: 9780076602186Carter, Cuevas, Day, Malloy
8,886 solutions

#### Nelson Functions 11

1st EditionISBN: 9780176332037Chris Kirkpatrick, Marian Small
1,275 solutions

#### Precalculus: A Right Triangle Approach

3rd EditionISBN: 9780321912763 (2 more)J. S. Ratti, Marcus S. McWaters
5,672 solutions

#### Precalculus with Limits

3rd EditionISBN: 9781133962885 (3 more)Larson
11,068 solutions