Matrix Multiplication is a binary operation that takes a pair of matrices, and produces another matrix. Numbers such as the real or complex numbers can be multiplied according to elementary arithmetic
If A is an n × m matrix and B is an m × p matrix,
the matrix product AB (denoted without multiplication signs or dots) is defined to be the n × p matrix
If the column and rows are in the same size it is defined.
EXAMPLE:
Wednesday, August 13, 2014
Matrix Subtraction
Matrix Subtraction- you can subtract two matrices (of the same size) by adding their corresponding entries.
EXAMPLES:
1.
2.
Given the following matrices, find A – Band A – C, or explain why you can not.
EXAMPLES:
1.
2.
Given the following matrices, find A – Band A – C, or explain why you can not.
- A and C are not the same size, since A is 2 × 3 and C is 2 × 2. So this subtraction is not defined.
A – C is not defined, because A and C are not the same size.
Matrix Addition
Matrix Addition is the operation of adding two matrices by adding the corresponding entries together.
EXAMPLE:
EXAMPLE:
Equality of Matrices
Two matrices are equal if all three of the following conditions are met:
Consider the three matrices shown below.
If A = B then we know that x = 34 and y = 54, since corresponding elements of equal matrices are also equal.
We know that matrix C is not equal to A or B, because C has more columns.
- Each matrix has the same number of rows.
- Each matrix has the same number of columns.
- Corresponding elements within each matrix are equal.
Consider the three matrices shown below.
If A = B then we know that x = 34 and y = 54, since corresponding elements of equal matrices are also equal.
We know that matrix C is not equal to A or B, because C has more columns.
- Two equal matrices are exactly the same.
- If rows are changed into columns and columns into rows, we get a transpose matrix. If the original matrix is A, its transpose is usually denoted by A' or At.
- If two matrices are of the same order (no condition on elements) they are said to be comparable.
- If the given matrix A is of the order m x n, then its transpose will be of the order n x m.
- Column matrix - a matrix that has only one column.
- Row matrix - a matrix that has only one row.
Kirchoff's Law
Kirchhoff's Law is an analysis of such a system uses two properties of electrical networks or two equalities that deal with the current and potential difference in the lumped element model of electrical circuits.
1. All current flowing into a junction must flow out of it.
Network Analysis
Network Analysis - composed of branches and junctions are used as models in many diverse fields such as economics, traffic analysis, and electrical engineering.
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