What is the difference between vector group equivalence and matrix equivalence

Two matrices A and B are equivalent. A can be transformed into B by finite elementary transformation

Vector group is equivalent, two vector groups can express each other

The specific analysis is as follows:

For each system of equations, it corresponds to an augmented matrix,
a11… a1n |b1
.|.
am1… amn|bn
I know that AXX in the front is a matrix composed of the coefficients of the system of equations. What is Bxx in the back?

Bxx is the value after the equal sign
It's like X1 + 2x2 + 5x3 = 10
10 in

What is the difference between vector and matrix in linear algebra?

Vector is a special type of matrix
That is, a matrix with only one row or column
They are called row matrix (row vector) and column matrix (column vector)
In addition, the matrix is expressed in order, such as a square matrix of order 2
Vectors are usually expressed in terms of dimensions, such as n-dimensional vectors
In a word, the essence of vector is matrix,
The operation law of all reference matrix calculation

It is known that the sum of the elements in each row of the real symmetric matrix A of order 3 is 4, and the vector a (- 4,2,2) ^ t is the solution of the system of homogeneous linear equations AX = 0,
And the sum of diagonal elements of matrix A is - 1, then (1) the eigenvalue of matrix A is?
(2) The eigenvectors belonging to the eigenvalues are?
(3) Matrix A is equal to?
The idea is not very clear

With the nature of eigenvalues and similar nature. Economic mathematics team to help you answer. Please timely evaluation

Let the sum of all elements of the third order matrix a be 2, and the vector α 1 = (- 1,1,1) t, α 2 = (2, - 1,1) t is the solution of the homogeneous linear equation AX = 0
Find a

Gauss elimination method is used to solve linear equations. Firstly, the augmented matrix is transformed into row ladder matrix. Secondly, the row spacing ladder matrix is transformed into row simplified ladder matrix,
The book says so, but I think (2) can be omitted

It's true that we don't need to change it into the row simplest form. Our goal is to solve the linear equations as long as we can solve the equations, but changing it into the row simplest form is convenient for us to see what the solution of the equations is

When a matrix is used to solve a system of linear equations, how can it be calculated after the augmented matrix is reduced to the simplest form? It is said in the book that some are regarded as free unknowns and some are not free unknowns. How can we get this?

It regards the column of the first non-zero element in the non-zero row as the constrained unknown quantity, and regards the rest of the unknown quantity as the free unknown quantity

Find the solution of linear equations. To what extent do you want to simplify the augmented matrix into the row simplest form

Non homogeneous linear equations AX = b
The augmented matrix can be transformed into ladder form by elementary row transformation

Determinant vector of linear algebraic matrix
It is known that a1a2a3a4 is a 4-dimensional non-zero column vector. Let a = (a1a2a3a4). If the fundamental solution system of AX = 0 is (1,0, - 2,0) t, then the fundamental solution system of a * x = 0 is () (c) a1a2a3 (d) a2a3a4. Why is option C wrong?

The three vectors of term C are linearly related, so they are not the basic solution system

The difference between determinant, matrix and vector is: determinant is?; matrix is?; vector is?

The essence of determinant is a number
A vector is an array
A matrix is a number matrix
The matrix can be divided into several row vectors or several column vectors

What is the difference between vector group equivalence and matrix equivalence