Matrices Flashcards
What is a matrix
A rectangular grid of numbers enclosed in brackets
What is the order of a matrix?
It’s shape/size eg. m x n where m is rows and n is columns.
Elements in a matrix
A specific number enclosed in a matrix. Denoted by aij
Where a is the matrix it’s in.
i is the row and j is the column
Gaussian elimination for 2 rows
Put equations in augmented matrix.
Manipulate rows by either multiplying/dividing or adding/subtracting multiples of other rows.
Goal is to have 0 in bottom left element. Then extract values of x and y from augmented matrix.
Gaussian elimination for 3 rows.
Similar to 2 except we have 3 variables and rows. Final row should be to have a right angled triangle of 0s in bottom left corner. Then extract information.
How to recognise redundancy during Gaussian elimination
When all of bottom lines elements are 0.
How to recognise inconsistency in Gaussian elimination.
When bottom lines elements are all 0 except answer.
How to work through Gaussian elimination with redundancy
Let z = a new variable and use to solve other variables.
How to work through Gaussian elimination with inconsistency.
We cannot.
Adding and subtracting matrices.
Add or subtract separate elements within that are in the same position in their respective matrices.
Multiplying matrices by a scalar
Multiply all elements by this scalar.
What types of matrices can me multiply together
Conformable matrices.
What makes to two matrices conformable
One on the right has the same number of columns as the one on left has rows.
How to multiply two conformable matrices.
We add products of rows on the left and columns on the right. We form new matrix. We use rows/columns that overlap for parts on our new matrix.
Notation for transpose of a matrix
A’ or A^T
