Chapter 6: Matrices Flashcards
What is a square matrix?
A matrix with the same amount of rows and columns
What is a zero matrix?
A matrix in which all elements are 0
What is an identity matrix?
A square matrix in which elements on the leading diagonal (top left to bottom right) are all 1 and the rest are 0.
e.g. |1 0|
|0 1|
How do you add/subtract matrices?
Add/subtract the corresponding elements in each matrix. You can only do this to matrices of the same size.
What does ‘nxm’ mean?
No of rows multiplied by no of columns
How do you multiply a matrix by a scalar?
Multiply each element of the matrix by the scalar
What is the rule for 2 matrices being multiplied together?
The first matrix has the same amount of columns as rows in the second
What is the determinant of 2x2 matrix M?
|a b|
|c d|
ad-bc
How do you know if a matrix is singular or not?
If detM=0, it is singular and it doesn’t have an inverse.
If detM≠0, it is non-singular and it has an inverse.
What is the determinant of 3x3 matrix M?
|a b c|
|d e f|
|g h i|
a|e f| - b |d f| + c |d e|
|h i| |g i| |g h|
What is a minor in a 3x3 matrix?
The 2x2 matrix that remains after the row and column that element have been crossed out.
What is the inverse of matrix M?
|a b|
|c d|
M⁻¹= 1/detM|d -b|
|-c a|
What is the transpose of a matrix?
Found by interchanging the rows and columns
What are the steps to inverting a 3x3 matrix M?
1) Find detM
2) Find the matrix of minors.
3) Form a matrix of cofactors by changing signs as shown below.
|+ - +|
| - + -|
|+ - +|
4) Transpose the matrix of cofactors by interchanging rows and columns. (Mᵀ)
The inverse of matrix M is given by the formula: M⁻¹=(1/detM) Mᵀ
What does A|x| = v also equal?
|y|
|z|
|x| = A⁻¹v
|y|
|z|
