Chapter 11: Q. 43 (page 741)

In Problems 43–50, use properties of determinants to find the value of each determinant if it is known that $|\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}| = 4$
role="math" localid="1647383304224" $|\begin{matrix} 1 & 2 & 3 \\ u & v & w \\ x & y & z \end{matrix}|$

Short Answer

Expert verified

The value of $|\begin{matrix} 1 & 2 & 3 \\ u & v & w \\ x & y & z \end{matrix}|$ is $- 4$

$|\begin{matrix} 1 & 2 & 3 \\ u & v & w \\ x & y & z \end{matrix}| = - 4$

Step by step solution

Step 1. Given information

The given determinant is

$|\begin{matrix} 1 & 2 & 3 \\ u & v & w \\ x & y & z \end{matrix}|$

Step 2. Solution

On comparing both determinants, it seems that the determinant $|\begin{matrix} 1 & 2 & 3 \\ u & v & w \\ x & y & z \end{matrix}|$ is obtained by interchanging the first and third row of determinant $|\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}|$

Property of determinant state that the value of a determinant changes sign if any two rows are interchanged.

Since $|\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}| = 4$

so the value of determinant $|\begin{matrix} 1 & 2 & 3 \\ u & v & w \\ x & y & z \end{matrix}| = - 4$

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In Problems 43–50, use properties of determinants to find the value of each determinant if it is known that $|\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}| = 4$
role="math" localid="1647383304224" $|\begin{matrix} 1 & 2 & 3 \\ u & v & w \\ x & y & z \end{matrix}|$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solution

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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=4role="math" localid="1647383304224" 123uvwxyz

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Geometry

Logic and Functions

Theoretical and Mathematical Physics

Mechanics 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 $|\begin{matrix} x & y & z \\ u & v & w \\ 1 & 2 & 3 \end{matrix}| = 4$
role="math" localid="1647383304224" $|\begin{matrix} 1 & 2 & 3 \\ u & v & w \\ x & y & z \end{matrix}|$