Linear AlgebraPlease show all work (a) Use row and column operations to calculate the determinant of the41 2 -33 31-1 3 -9156matrix A=28

NOTE: Refresh your page if you can't see any equations. . by interchange, the row determinant will…

Answered: (a) Use row and column operations to…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Linear Algebra

Please show all work

(a) Use row and column operations to calculate the determinant of the
4
1 2 -3
3 3
1
-1 3 -9
1
56
matrix A
=
2
8

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.

Expert Solution

Step 1

NOTE: Refresh your page if you can't see any equations.

$A=\begin{pmatrix}4&-1&2&-3\\ 2&3&3&1\\ 8&-1&3&-9\\ 5&5&6&1\end{pmatrix}$

$\:R_1\:\leftrightarrow \:R_3$

by interchange, the row determinant will negative

$=-1\begin{pmatrix}8&-1&3&-9\\ 2&3&3&1\\ 4&-1&2&-3\\ 5&5&6&1\end{pmatrix}$

$R_2-\frac{1}{4}\cdot \:R_1\rightarrow R_2$

$R_3-\frac{1}{2}\cdot \:R_1 \to R_3$

$R_4-\frac{5}{8}\cdot \:R_1 \rightarrow R_4$

by adding or subtracting, one row from another row, there is no change in a determinant

$=-1\begin{pmatrix}8&-1&3&-9\\ 0&\frac{13}{4}&\frac{9}{4}&\frac{13}{4}\\ 0&-\frac{1}{2}&\frac{1}{2}&\frac{3}{2}\\ 0&\frac{45}{8}&\frac{33}{8}&\frac{53}{8}\end{pmatrix}$