Evaluate the determinant to determine whether the equation is true or false. 1 x3 y y = (y – x)(z – x)(z – y) z3 1 1 Evaluate the determinant and the expression on the right side of the equation. (Simplify your answers completely.) 1 x3 1 y3 z3 y %3D (y - x)(z – x)(z - y) = Is the equation true or false? O True O False
Evaluate the determinant to determine whether the equation is true or false. 1 x3 y y = (y – x)(z – x)(z – y) z3 1 1 Evaluate the determinant and the expression on the right side of the equation. (Simplify your answers completely.) 1 x3 1 y3 z3 y %3D (y - x)(z – x)(z - y) = Is the equation true or false? O True O False
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
2
![**Evaluate the Determinant to Determine Truth of the Equation**
Evaluate the determinant to determine whether the equation is true or false.
\[
\begin{vmatrix}
1 & x & x^3 \\
1 & y & y^3 \\
1 & z & z^3 \\
\end{vmatrix}
= (y-x)(z-x)(z-y)
\]
**Task:** Evaluate the determinant and the expression on the right side of the equation. Simplify your answers completely.
\[
\begin{vmatrix}
1 & x & x^3 \\
1 & y & y^3 \\
1 & z & z^3 \\
\end{vmatrix}
= \boxed{\quad}
\]
\[
(y-x)(z-x)(z-y) = \boxed{\quad}
\]
Is the equation true or false?
- ⭕ True
- ⭕ False
**Instructions:** Fill in the boxes with the simplified expressions for the determinant and the product on the right side of the equation. Then select whether the equation is true or false based on your calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98ab6ef6-0d6b-4611-9e42-e18dbe67af78%2F3e81aeb7-789c-4267-b65b-c12f3cddf3a1%2F5izbj5n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Evaluate the Determinant to Determine Truth of the Equation**
Evaluate the determinant to determine whether the equation is true or false.
\[
\begin{vmatrix}
1 & x & x^3 \\
1 & y & y^3 \\
1 & z & z^3 \\
\end{vmatrix}
= (y-x)(z-x)(z-y)
\]
**Task:** Evaluate the determinant and the expression on the right side of the equation. Simplify your answers completely.
\[
\begin{vmatrix}
1 & x & x^3 \\
1 & y & y^3 \\
1 & z & z^3 \\
\end{vmatrix}
= \boxed{\quad}
\]
\[
(y-x)(z-x)(z-y) = \boxed{\quad}
\]
Is the equation true or false?
- ⭕ True
- ⭕ False
**Instructions:** Fill in the boxes with the simplified expressions for the determinant and the product on the right side of the equation. Then select whether the equation is true or false based on your calculations.
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