Matrices Flashcards
What equation is used to work out how many parameters will be in the general solution of a matrix system?
of variables - # of rows in REF = # of parameters
What effect does swapping rows have on the determinant of a matrix?
sign change
What effect does multiplying by a scalar have on the determinant of a matrix?
multiply det by scalar
What effect does adding a scalar multiple of a row to another row have on the determinant of a matrix?
no change
What is the determinant of diag(a11, a22, … , ann)?
a11 x a22 x … x ann
If a matrix has a zero row, what is its det?
0
How is the adjugate (or adjoint) of a matrix found?
i) replace each entry in the matrix by the cofactor
ii) take the transpose of the resulting matrix
What is the equation to find the inverse of a matrix?
A^-1 = (1/detA) x adj A (det A =/= 0)
When is a matrix symmetric?
A^T = A
When is a matrix skew-symmetric?
A^T = -A
When is a matrix idempotent?
A^2 = A
What is the trace of a matrix?
The trace Tr(A) of a square n×n matrix A is defined to be the sum of the entries on its main diagonal.
