Matrices concept confusion....

In summary, a matrix is a rectangular array of numbers, symbols, or expressions used in mathematics and science. It is used for solving equations, representing transformations, and analyzing data. The main difference between a matrix and a vector is their dimensions, with vectors being one-dimensional arrays. To add or multiply matrices, they must have the same dimensions and the operations involve corresponding elements. Matrices have various real-life applications, including in computer graphics, economics, and chemistry.
  • #1
Clara Chung
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14
In the photo that is a matrix B. B^3 + B = 2B^2 +2I from calculations. But why not B must be equal to 2I, the reason is as follow,
B(B^2 + I ) = 2(B^2 +I)
B(B^2 + I)(B^2 + I)^(-1) = 2I (B^2 + I)(B^2 + I)^(-1)
so B = 2I why is my concept wrong? please explain to me.
 

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  • #2
Your concept assumes that the matrix (B^2 + I)^-1 exists. But there is also the possibility that the matrix (B^2 + I) is singular and has no inverse, which is the case for your matrix B.
 
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1. What is a matrix?

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns, often used to represent and manipulate data in mathematics and science.

2. How are matrices used in science?

Matrices are used in science for a variety of purposes, including solving systems of equations, representing transformations in geometry, and analyzing data in statistics.

3. What is the difference between a matrix and a vector?

A matrix is a rectangular array of numbers or symbols, while a vector is a one-dimensional array. Vectors can be thought of as special cases of matrices, with only one row or one column.

4. How do you add or multiply matrices?

To add or multiply matrices, they must have the same dimensions (same number of rows and columns). Addition is performed by adding corresponding elements, while multiplication involves multiplying corresponding elements and summing the products.

5. What are some real-life applications of matrices?

Matrices have many real-life applications, such as in computer graphics, where they are used to transform and manipulate images. They are also used in economics to model and analyze systems of equations, and in chemistry to represent and solve chemical reactions.

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