Eng Math II

Det of a triangular matrix

product of the main diagonal

det(A^T)

= det(A)

det(2A)

Rule: Multiplying an n x n matrix by a scalar k multiplies its determinant by kⁿ

A is 3×3 matrix so det(2A) = 2³det(A)

det(AB)

det(A)det(B)

det(A^-1)

=1/(det(A))

find the det(A) if 2 rows were swapped

= - det(A₀)

how to check if a matrix is one-to-one

if it has a pivot in every column

what do the number of pivots tell you

which IR space it is in

Col A = span {a₁, a₂, a₃, a₄}

all pos linear combinations of the columns. Col A give all pos outcomes of Ax

Basis of Col A

Pivot cols of reduced rows but of og A