Solve X', X for Y: Matrix Algebra Help

In summary, the conversation discusses finding the values of X and Y based on given equations involving matrices. However, there is difficulty in solving for X due to four unknowns and only three equations. Clarification is needed on the number of rows in the matrix X.
  • #1
pinto89a
5
0
Find X if

X' * X =
(50, 300)
(300, 1000)

Then find Y if
Y * X =
(300, 2000)

Problem is that when I try to solve for X (or X') first, I get three equations with four unknowns (a11, a12, a21, a22). Any help?
 
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  • #2
I'm not sure what your notation is. Does X' mean adjoint, transpose, or what? You should have 4 equations in 4 unknowns, however, since each entry of the resultant matrix is found by multiplying elements of the individual matrices (and there are 4 elements in the resultant matrix).
 
  • #3
Yes, the ' is transpose.

I get
a11 ^2 + a21 ^2 = 50
a11 * a12 + a21 * a22 = 300
a12 ^2 + a22 ^2 = 1000

but I can't get the fourth equation?
 
  • #4
The matrix X must be 2 columns, but how many rows? Is X a simple 2x2 matrix?
 

1. What is matrix algebra?

Matrix algebra is a branch of mathematics that deals with the manipulation and operations of matrices, which are rectangular arrays of numbers or symbols. It includes techniques for solving systems of linear equations, calculating determinants and eigenvalues, and performing matrix transformations.

2. How do I solve for X in a matrix equation?

To solve for X in a matrix equation, you must use inverse operations to isolate X on one side of the equation. This involves performing the same operations on both sides of the equation, such as addition, subtraction, multiplication, and division. The end result will be the value of X that satisfies the equation.

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Yes, matrix algebra is commonly used in data analysis to perform operations on large datasets. It can help with tasks such as data transformation, dimensionality reduction, and pattern recognition. Many statistical and machine learning models also use matrix algebra as a fundamental tool.

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The basic operations in matrix algebra include addition, subtraction, multiplication, and division. Addition and subtraction are performed element-wise, meaning that each element in one matrix is added or subtracted from the corresponding element in another matrix. Multiplication involves multiplying each element in a row of one matrix by each element in a column of another matrix and summing the products. Division of matrices is not defined, but division by a scalar (single number) is possible.

5. How can I apply matrix algebra in real life?

Matrix algebra has numerous real-life applications, such as in engineering, physics, economics, and computer graphics. It can be used to model and solve complex systems, analyze data, and make predictions. Some common examples include using matrix algebra to optimize production processes, forecast stock prices, or create 3D animations.

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