Question

Use properties of determinants to find the value of each determinant if it is known that. $\left|\begin{array}{lll}x & y & z \\ u & v & w \\ 1 & 2 & 3\end{array}\right|=4$ $$\left|\begin{array}{lll}x & y & z \\ u & v & w \\ 2 & 4 & 6\end{array}\right|$$

Name: Problem 44, Chapter 10: Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry
Uploaded: 2022-01-09T14:20:54-08:00
Duration: 35 s
Channel: Hannah Wilds
Description: Use properties of determinants to find the value of each determinant if it is known that. | x y z u v w 1 2 3 |=4 | x y z u v w 2 4 6 |

   Use properties of determinants to find the value of each determinant if it is known that.
$\left|\begin{array}{lll}x & y & z \\ u & v & w \\ 1 & 2 & 3\end{array}\right|=4$
$$\left|\begin{array}{lll}x & y & z \\ u & v & w \\ 2 & 4 & 6\end{array}\right|$$

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Michael Sullivan,… 3rd Edition

Chapter 10, Problem 44

Instant Answer

Solved by Expert Hannah Wilds

01/09/2022

Step 1

The determinant of a matrix is a special number that can be calculated from a square matrix. It is denoted as det(A) or |A| where A is the matrix. Show more…

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Use properties of determinants to find the value of each determinant if it is known that. $\left|\begin{array}{lll}x & y & z \\ u & v & w \\ 1 & 2 & 3\end{array}\right|=4$ $$\left|\begin{array}{lll}x & y & z \\ u & v & w \\ 2 & 4 & 6\end{array}\right|$$

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Key Concepts

Linearity with Respect to Rows

Determinants are linear in each row, meaning that if a row of a matrix is replaced by a linear combination (or a scalar multiple) of another row, the overall determinant will adjust correspondingly. In this context, if one row of a matrix is replaced by a scalar multiple of its previous form, the determinant is scaled by that same scalar.

Scalar Multiplication of a Row

One of the fundamental properties of determinants is that if a single row (or column) of a matrix is multiplied by a scalar, then the determinant of the matrix is also multiplied by that scalar. This property is crucial in simplifying determinant computations by factoring out common multipliers from a row.

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