Matrices

how to find the determinant

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how to find the inverse of 2x2 matrix

what is the minor of an element

the determinant of the matrix obtained by deleting the row and column in which that element lies

when is a matrix singular and what does this mean?

when detM=0, so this matrix doesn't have an inverse

how to find the determinant

a(minor of a) -b(minor of b) +c(minor of c)

what is the transpose of a matrix?

changing the columns into rows, and vice versa

acronym and steps to inverse the 3x3 matrix A

Driving Monkeys Can’t Travel Fast

detA, matrix of minors, matrix of cofactors, transpose, apply the formula

how to form the matrix of cofactors

switch the sides' signs, keep the corners constant (and the middle)

the final formula in finding the inverse of a 3x3 matrix

how to form the 3x3 matrix in the simultaneous equations method

each row is the coefficients of x, y and z in each equation

how to solve matrix simultaneous equations

(matrix of coefficients)\*(x,y,z matrix)=(matrix of answers to sim.eqs)

when do the planes meet at a single point

when the determinant is __**not**__ 0

when do the planes form a sheaf

det=0, reduced to two equations which are consistent, the three equations aren’t multiples of each other

when are the planes the same plane

all three **equations** are multiples of each other

when do the planes form a prism

det=0, when reduced to two equations they are inconsistent, no rows of the matrix are multiples of each other

when are only two planes parallel

when **only** two rows of the matrix are multiples of each other

when are all the planes parallel

when all rows of the matrix are multiples of each other, but __**not**__ the equations

what does the determinant of a transformation matrix represent

area scale factor

a rotation of A about the x axis

a rotation of θ about the y axis

\

a rotation of C about the z axis

det(AB)=

(detA)(detB)

(AB)⁻¹=

B⁻¹A⁻¹ (think of order of geometric transformations)