System of linear equations - matrix form
Any system of linear equations can be written as the matrix equation.
So a system of linear equations
|a11x1 + a12x2 + ... + a1nxn = b1|
|a21x1 + a22x2 + ... + a2nxn = b2|
|am1x1 + am2x2 + ... + amnxn = bm|
consisting of m linear equations with n unknowns can be written as a matrix equation:
Ax = b
|A =||a11||a12||...||a1n||; x =||x1||; b =||b1|
Matrix A is the matrix of coefficient of a system of linear equations, the column vector x is vector of unknowns variables, and the column vector b is vector of a system of linear equations values.
N.B. If the i-th row of the system of linear equations is not the variable xj, it means that it multiplier is zero, ie aij = 0.
Example of matrix form of system of linear equations
Example 1.Write system of linear equations in matrix form:
|4x1 + x2 - x3 - x4 = 3|
|-x1 + 3x3 - 2x4 = 5|
|6x1 + 2x2 + 4x3 = 2|
|2x2 - x3 + x4 = 0|
Solution: System of linear equations in matrix form:
MatrixMatrix Definition. Main informationSystem of linear equations - matrix formTypes of matricesMatrix scalar multiplicationAddition and subtraction of matricesMatrix multiplicationTranspose matrixElementary matrix operationsDeterminant of a matrixMinors and cofactors of a matrixInverse matrixLinearly dependent and independent rowsRank of a matrix
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