4. Matrix Operations in Excel.
Matrix Manipulations: Vectors, Matrices, and Arrays. How Excel Handles
Matrix Math. Basic Matrix Operations. Solving Systems of Linear Equations.
Matrix Manipulations: Vectors, Matrices, and Arrays.
In this section we consider the topic of Vectors, Matrices and Arrays and
their application in solving Linear Equations and other linear algebra
problems.
Simultaneous linear equations occur frequently in engineering in such areas
as heat conduction, molecular diffusion, fluid mechanics and in data
regression. Excel’s “Solver” feature will be used in a later chapter to solve
more complicated linear and nonlinear systems of equations.
Generally the term matrix (from mathematics) and array (from Excel) can
be used interchangeably to refer to data organized in row and column
fashion. Matrices consisting of a single row or a single column are called
vectors. Even though the functions are “named” with matrix there is no
help in Excel under “matrix” only “array”.
Typical Linear Equation Set and Corresponding Matrices
a11x1 + a12x2 +a13x3 = b1
a21x1 + a22x2 +a23x3 = b2
a31x1 + a32x2 +a33x3 = b3
Where [A] =
31 32 33
21 22 23
11 12 13
a a a
a a a
a a a
[X] =
3
2
1
x
x
x
[B] =
3
2
1
b
b
b
Is represented in math as
[A][X] = [B]
and has the solution [X] = [A]-1 [B]
How Excel