Matrices

studied byStudied by 31 people
5.0(1)
get a hint
hint
<p>how to find the determinant</p>

how to find the determinant

1 / 22

23 Terms

1
<p>how to find the determinant</p>

how to find the determinant

ad-bc

New cards
2
<p>how to find the inverse of 2x2 matrix</p>

how to find the inverse of 2x2 matrix

knowt flashcard image
New cards
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

New cards
4

when is a matrix singular and what does this mean?

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

New cards
5
<p>how to find the determinant</p>

how to find the determinant

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

New cards
6

what is the transpose of a matrix?

changing the columns into rows, and vice versa

New cards
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

New cards
8

how to form the matrix of cofactors

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

New cards
9

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

knowt flashcard image
New cards
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

New cards
11

how to solve matrix simultaneous equations

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

New cards
12

when do the planes meet at a single point

when the determinant is not 0

New cards
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

New cards
14

when are the planes the same plane

all three equations are multiples of each other

New cards
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

New cards
16

when are only two planes parallel

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

New cards
17

when are all the planes parallel

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

New cards
18

what does the determinant of a transformation matrix represent

area scale factor

New cards
19

a rotation of A about the x axis

knowt flashcard image
New cards
20

a rotation of θ about the y axis

<p></p>
New cards
21

a rotation of C about the z axis

knowt flashcard image
New cards
22

det(AB)=

(detA)(detB)

New cards
23

(AB)⁻¹=

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

New cards

Explore top notes

note Note
studied byStudied by 1 person
Updated ... ago
5.0 Stars(1)
note Note
studied byStudied by 27 people
Updated ... ago
5.0 Stars(1)
note Note
studied byStudied by 2 people
Updated ... ago
5.0 Stars(1)
note Note
studied byStudied by 9 people
Updated ... ago
5.0 Stars(1)
note Note
studied byStudied by 6 people
Updated ... ago
5.0 Stars(1)
note Note
studied byStudied by 6 people
Updated ... ago
5.0 Stars(1)
note Note
studied byStudied by 4 people
Updated ... ago
5.0 Stars(1)
note Note
studied byStudied by 8360 people
Updated ... ago
4.7 Stars(31)

Explore top flashcards

flashcards Flashcard59 terms
studied byStudied by 102 people
Updated ... ago
5.0 Stars(1)
flashcards Flashcard300 terms
studied byStudied by 17 people
Updated ... ago
5.0 Stars(1)
flashcards Flashcard30 terms
studied byStudied by 3 people
Updated ... ago
5.0 Stars(1)
flashcards Flashcard71 terms
studied byStudied by 10 people
Updated ... ago
5.0 Stars(3)
flashcards Flashcard90 terms
studied byStudied by 3 people
Updated ... ago
5.0 Stars(2)
flashcards Flashcard31 terms
studied byStudied by 32 people
Updated ... ago
4.7 Stars(3)
flashcards Flashcard67 terms
studied byStudied by 2 people
Updated ... ago
5.0 Stars(1)
flashcards Flashcard112 terms
studied byStudied by 23 people
Updated ... ago
5.0 Stars(1)