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Matrixes & Linear transformations
How do you write the size of a matrix?
n x m
Where n = no.of rows and m = no.of columns
What is a square matrix?
A matrix where n(rows) and m (columns) are the same.
What is a zero matrix and how is it denoted?
A zero matrix is a matrix in which all elements are zero. It is denoted by 0nxm.
How do you add/subtract matrices?
(a b) ± (c d) = (a±c b±d)
Add/subtract corresponding elements, (can only add/subtract matrices of the same size)
What is an Identity matrix and how is it denoted?
A square matrix where elements on leading diagonal are 1, and all remaining are 0. It acts as a 1. It is denoted Ik, where k is n and m.
Matrices can be multiplied if…
the no.of columns in the first is equal to the no.of rows in the second.
What is the size of the product matrix when multiplying 2 matrices?
If multiplying matrix with size nxm with matrix size mxp, the product matrix will be of size nxp.
When multiplying two matrices, workout each element by…
Multiply the first element of that row in first matrix with first element of that column in the second matrix. Then the add that to the second element in row of first matrix with second element of column in second matrix, etc.
How to calculate the determinant for a 2×2 matrix?
ad - bc
A matrix is singular if…
the determinant is equal to zero
A matrix is non-singular if…
the determinant is not equal to zero
How to calculate the determinant of a 3×3 matrix?
What is the minor or an element (in a 3×3 matrix)?
The determinant of the 2×2 matrix remaining after crossing out the row and column the element lies on.
A matrix times it’s inverse is always…
Identity matrix
MM-1= I and M-1M= I
Instead of dividing matrices, we…
Multiply by its inverse. (Think of it as rather than ÷2, multiply by 1/2)
For 2×2 matrix M, the inverse is…
Since order matters when working with matrices, choosing between…
Pre-multiplying (infront) and post-multiplying (after) is crucial. (Keeping in mind MM-1= I)
Proving A = A-1 is equivalent to proving…
(xA)
A2 = I
