Chapter 11: Q. 46 (page 741)

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

Short Answer

Expert verified

The value of the determinant is $4$ .

Step by step solution

Step 1. Given Information

We are given,

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

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

We have to solve the given determinant using properties of determinant.

Step 2. Solving the determinant

Using subtraction of determinant, we get

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

Since the two rows of second determinant is same, so

$|\begin{matrix} 1 & 2 & 3 \\ x - u & y - v & z - w \\ u & v & w \end{matrix}| = |\begin{matrix} 1 & 2 & 3 \\ x & y & z \\ u & v & w \end{matrix}| - 0$

Interchanging the rows, we get

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

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solving the determinant

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In Problems 43–50, use properties of determinants to find the value of each determinant if it is known thatxyzuvw123=4123x-uy-vz-wuvw

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solving the determinant

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Probability and Statistics

Discrete Mathematics

Geometry

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