(Linear algebra)Pls answer question asapWrite work neatly and box final answersThanks **Matrix Determinant Calculation Using Cofactors**In this exercise, we will use expansion by cofactors to find the determinant of the following matrix:\[\begin{bmatrix}w & x & y \\21 & 27 & -18 \\-24 & 18 & -10 \\\end{bmatrix}\]To solve, we will expand across the first row (containing the variables \(w\), \(x\), and \(y\)):\[ \text{Determinant} = \boxed{\phantom{-}} w + \boxed{\phantom{-}} x + \boxed{\phantom{-}} y \]In this equation, each box will be filled with the appropriate cofactor calculation to determine the value.

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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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**Matrix Determinant Calculation Using Cofactors**

In this exercise, we will use expansion by cofactors to find the determinant of the following matrix:

\[
\begin{bmatrix}
w & x & y \\
21 & 27 & -18 \\
-24 & 18 & -10 \\
\end{bmatrix}
\]

To solve, we will expand across the first row (containing the variables \(w\), \(x\), and \(y\)):

\[ \text{Determinant} = \boxed{\phantom{-}} w + \boxed{\phantom{-}} x + \boxed{\phantom{-}} y \]

In this equation, each box will be filled with the appropriate cofactor calculation to determine the value.

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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