UNIT 3 Flashcards
If a matrix is order 2x3 how many rows and colums does it have?
2 rows and 3 columns
What element does A12 refer to?
1st row second column
What is a square matrix?
Has the same number of rows as columns
Where does the main diagonal run?
Top left to bottom right
What is a zero matrix?
Each element is Zero
What is an equal matrix?
When the order and each element is equal
What is the transpose of a matrix?
When the rows become columns.
When is a matrix symmetric?
When matrix ‘A’ = The transpose of matrix ‘A’
When is a matrix skew-symmetric?
When the transpose of matrix ‘A’ = -A and the main diagonal consists of zeros.
What is the condition for adding matrices together?
They must be in the same order
How do you subtract matrices?
Use addition but add the negative of the matrix you are taking away. e.g A-B= A+ (-B)
How do you multiply a matrix by a real number?
Multiply each element by the number
What are the transpose properties?
(A’)’=A
(A+B)’=A’+B’
What is the condition for a product of two matrices to exist?
The number of columns in the first matrix has to equal the number of rows in the second matrix
When calculating the product of two vectors what do the outside numbers indicate? (3x2 and 2x4)
The order of the resulting matrix (3x4)
(AB)C=
A(BC)
What does A(B+C) =
AB + AC
PQ does not equal
QP
What is the identity matrix? (I)
A square matrix where the main diagonal is 1’s and the rest of the numbers are zero’s
If an inverse matrix exists what is AB?
=BA=I
How can you determine the inverse of a 2x2 matrix?
1/(ad-bc) {d-b}
{-ca}
What is the determinant for a 2x2 matrix?
ad-bc
What does it mean if the determinant of a 2x2 matrix is 0?
It is called a singular matrix because it does not have an inverse
What does it mean if the determinant of a 2x2 matrix is not 0?
It has an inverse and is called a non-singular matrix
(AB)^-1=
(B^-1)(A^-1)
det (AB) =
det A x det B
What are the stages of finding the inverse to a matrix using E.R.O’s?
Make top left entry 1 and the entries below it 0
Make the second entry in the main diagonal 1 and the entry below it 0
Make the last entry of the main diagonal 1
Make the entries above this 1 zero
Make the last number that isn’t in the main diagonal a zero
A(A)-1 =
I
What is AX=B rearranged to? (when finding an inverse matrix)
X=A^-1 B
How do you find the transpose of a 3x3 matrix?
Do the determinant calculation thing but for all rows to form a matrix, no co efficients. Signs are alternating, starting with positive.
How do you calculate the inverse of a 3x3 matrix using the transpose and the determinant?
1/det A multiplied by the transpose.
How do you find the solution of a 3x3 matrix using the inverse?
X=A^-1 B Where B is the column matrix consisting of the last values in the equations (solutions)
