Matrices and Determinants
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1
Who discovered matrices and when were they discovered?
Cayley, a French mathematician, discovered matrices in the year 1860.
2
What are the importance of matrices?
1. Useful in branches of applied mathematics.
2. Enable us to consider an array of many numbers as one object.
3. Treatment of linear equations.
2. Enable us to consider an array of many numbers as one object.
3. Treatment of linear equations.
3
What is the most important application of matrices?
The treatment of linear equations.
4
_ is a rectangular array consisting of elements written in rows and columns usually enclosed by a bracket.
Matrix
5
If the matrix has m rows and n columns, the matrix is a _ matrix.
mxn matrix
6
Matrices are denoted by _
A single capital letter.
7
The elements from A11 to Ann is in the diagonal called the _
Principal/Leading/Main Diagonal
8
What are the 8 types of matrices?
Square
Zero/Null
Identity
Row
Column
Diagonal
Scalar
Triangular
Zero/Null
Identity
Row
Column
Diagonal
Scalar
Triangular
9
The number of rows and columns are equal (m=n)
Square Matrix
10
All elements are zero, usually denoted by zero.
Zero/Null Matrix
11
Square matrix where all diagonal elements are "1" and others are "0".S
Identity Matrix
12
Having only one row and "n" columns. Also called a row vector.
Row Matrix
13
Having only one column and "m" rows. It is also called a column vector.
Column Matrix
14
Every term off the main diagonal is zero.
Diagonal Matrix
15
Square matrix where all the terms in the main diagonal are equals.
Scalar Matrix
16
Square matrix whose elements above or below the main diagonal are zero.
Triangular Matrix
17
What are the types of matrix operations?
Equality of Matrices
Addition and Subtraction of Matrices
Multiplication of Matrix by Scalar
Multiplication of Matrix by Matrix
Transpose of Matrix (?)
Addition and Subtraction of Matrices
Multiplication of Matrix by Scalar
Multiplication of Matrix by Matrix
Transpose of Matrix (?)
18
(Equality of Matrices) Two matrices are only equal when:T
They're the same order.
Each element of A is equal to each corresponding element of B.
Each element of A is equal to each corresponding element of B.
19
(Addition and Subtracation of Matrices) Two matrices can be added if:
They are the same order.
20
(Multiplication of a Matrix by Scalar) The matrices A and B can only be multiplied in the order AB if:
The number of columns of A is equal to the number of rows of B.
21
What are the properties of multiplication by scalar?
Associative.
Not commutative.
Cancellation law is untrue.
Transpose of a product is transposed factors in reverse order.
Not commutative.
Cancellation law is untrue.
Transpose of a product is transposed factors in reverse order.
22
(Transpose of Matrix) The transpose of matrix A denoted by AT is obtained by:
Interchanging the rows and columns of matrix A.
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