Cpt Qwark said:Homework Statement
\begin{array}{rrr|r} -1 & 2 & -1 & -3 \\ 2 & 3 & α-1 & α-4 \\ 3 & 1 & α & 1 \end{array}
[tex]α∈ℝ[/tex]
for the augmented matrix, what value of α would make the system consistent?
Homework Equations
N/A
Answer: α=2
The Attempt at a Solution
I know that the system has to have an infinite or unique amount of solutions to be consistent and you have to perform Gaussian elimination?
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. It is commonly used in mathematics and other scientific fields to represent and manipulate data.
To multiply two matrices, the number of columns in the first matrix must match the number of rows in the second matrix. Then, you can multiply each element of the first row with each element of the first column in the second matrix, and add the products. This process is repeated for each row and column combination, resulting in a new matrix with the same number of rows as the first matrix and the same number of columns as the second matrix.
The identity matrix is a special square matrix with 1s along the main diagonal and 0s everywhere else. When multiplied with another matrix, the identity matrix acts like the number 1 in regular multiplication, leaving the other matrix unchanged.
Matrices are used in many scientific fields, such as physics, engineering, and computer science. They are used to represent and solve systems of linear equations, analyze data in statistics, and perform transformations in computer graphics and image processing.
Yes, matrices can be used to solve various types of word problems in mathematics. They can represent a system of equations and be used to find the values of unknown variables. They can also be used to solve optimization problems and model real-world situations.