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Hint

1

how to find the determinant

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2

how to find the inverse of 2x2 matrix

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3

what is the minor of an element

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

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4

when is a matrix singular and what does this mean?

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

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5

how to find the determinant

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

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6

what is the transpose of a matrix?

changing the columns into rows, and vice versa

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7

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

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8

how to form the matrix of cofactors

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

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9

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

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10

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

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

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11

how to solve matrix simultaneous equations

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

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12

when do the planes meet at a single point

when the determinant is __ not__ 0

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13

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

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14

when are the planes the same plane

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

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15

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

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16

when are only two planes parallel

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

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17

when are all the planes parallel

when all rows of the matrix are multiples of each other, but __ not__ the equations

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18

what does the determinant of a transformation matrix represent

area scale factor

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19

a rotation of A about the x axis

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20

a rotation of θ about the y axis

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21

a rotation of C about the z axis

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22

det(AB)=

(detA)(detB)

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23

(AB)⁻¹=

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

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