Week 3: Matrices Flashcards
Is matrix addition commutative or associative?
Both
A+B=B+A (commutative)
A+(B+C) = (A+B) +C (associative)
Can a 3x2 and a 4x3 matrix be added together?
Why/why not?
No because they do not have the same order (size).
What happens when a matrix is multiplied by a scalar?
The scalar multiplies across all the components of the matrix.
What is the zero matrix?
A matrix with all components 0.
How is a matrix named?
A matrix is named by stating the “no. of rows by no. of columns”
For example a matrix that has 3 rows and 2 columns would be called a “3 by 2 matrix”
Is matrix multiplication commutative?
No. This means AB ≠ BA.
Under what conditions is matrix multiplication possible?
A = (m x n) B = (p x q)
AB = (m x n)(p x q)
Only possible if n = p
Resulting matrix size is m x q
Is matrix multiplication associative?
Yes.
A(BC) = (AB)C
Is
(kA)B = A(kB)
true?
Yes. It does not matter in which order a scalar is multiplied across matrices.
What is the identity matrix?
An identity matrix is a matrix that has diagonal components equal to one and all other components equal to zero.
What property does the identity matrix have?
When multiplied by the identity vector the original matrix stays the same.
AI = IA = A
What is the transpose matrix?
A transpose matrix has the columns and rows switched. The first row becomes the first column (left-right becomes up-down) or vice versa.
What is the determinant of a matrix?
It is the scalar value of a matrix.
Do all matrices have an inverse?
No. Some matrices do not have an inverse matrix.
What is a procedure to find the inverse matrix other than row operations?
- Find the determinant of the matrix.
- Find the cofactors of the matrix.
- Find the adjugate, transpose of the cofactor matrix.
- Sub into the equation
A^(-1) = [1/detA] x [(A^C)^T]
