Chapter 11: Q. 44 (page 741)

In Problems 43–50, use properties of determinants to find the value of each determinant if it is known that $|\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}| = 4$
$|\begin{matrix} x & y & z \\ u & v & w \\ 2 & 4 & 6 \end{matrix}|$

Short Answer

Expert verified

The value of the determinant $|\begin{matrix} x & y & z \\ u & v & w \\ 2 & 4 & 6 \end{matrix}|$ is $8 .$

$|\begin{matrix} x & y & z \\ u & v & w \\ 2 & 4 & 6 \end{matrix}| = 8$

Step by step solution

Step 1. Given information

The given determinant is

$|\begin{matrix} x & y & z \\ u & v & w \\ 2 & 4 & 6 \end{matrix}|$

Step 2. Value of determinant

Use the property of determinant and take $2$ common form last row of determinants

$|\begin{matrix} x & y & z \\ u & v & w \\ 2 & 4 & 6 \end{matrix}| = |\begin{matrix} x & y & z \\ u & v & w \\ 2 (1) & 2 (2) & 2 (3) \end{matrix}| = 2 |\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}| = 2 \times 4 = 8$

So the value of the determinant role="math" localid="1647384410681" $|\begin{matrix} x & y & z \\ u & v & w \\ 2 & 4 & 6 \end{matrix}|$ is $8$ .

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In Problems 43–50, use properties of determinants to find the value of each determinant if it is known that $|\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}| = 4$
$|\begin{matrix} x & y & z \\ u & v & w \\ 2 & 4 & 6 \end{matrix}|$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Value of determinant

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In Problems 43–50, use properties of determinants to find the value of each determinant if it is known that xyzuvw123=4xyzuvw246

Short Answer

Step by step solution

Step 1. Given information

Step 2. Value of determinant

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Theoretical and Mathematical Physics

Pure Maths

Calculus

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

In Problems 43–50, use properties of determinants to find the value of each determinant if it is known that $|\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}| = 4$
$|\begin{matrix} x & y & z \\ u & v & w \\ 2 & 4 & 6 \end{matrix}|$