Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Linear Algebra > Test 1 prep > Flashcards

Test 1 prep Flashcards

1
Q

3 types of possible solutions:

A

1 ) Unique solution
2 ) Infinite solution
3 ) No solution

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Unique and infinite solutions are ______ solutions

A

consistent

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

No solution is _________

A

inconsistent

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Difference between REF and RREF:

A

In RREF, the entries aside from leading ones have to be zeros whereas in REF, we only need leading ones as the first entry of a row

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

True or false: a matrix can have multiple REFs, but only a unique RREF.

A

True

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

“Number of leading variables of a matrix is called the _______ of that matrix”

A

rank (represented as IR^n)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

In the parametric solutions, there are 2 types of variables:

A

1 ) Leading variables
2 ) Free variables

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Only a square n x n matrix will have a main _______

A

diagonal

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Entries of a matrix are represented as:

A

a subscript ij

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

In a subscript ij, what does ij represent:

A

i = row
j = column

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Matrix product can only be achieved if:

A

nº of columns in A is identical to nº of rows in B

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What is the proper way of writing a system if linear equations in matrix form?

A

AX = b

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

What is a matrix transpose?

A

The interchange of rows and columns

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What are the 3 properties of AA^T or A^TA?

A

1 ) products are always square matrices
2 ) products are always symmetrical matrices
3 ) entries of the main diagonal are always positive

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What is the trace of a matrix?

A

Sum of main diagonal entries

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

tr(A+B) =

A

tr(A) + tr(B)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

True or false: tr(A) = tr(A^T)

A

True

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

tr(k*A) =

A

k*tr(A)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

tr(AB) =

A

tr(BA)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

A + B =

A

B + A

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

(A + B) + C =

A

A + (B + C)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

In general, AB does not =

A

BA

23
Q

(AB)C =

A

A(BC)

24
Q

A(B + C) =

A

AB + AC (right distribution)

25
Q

(A + B)C =

A

AC + BC (left distribution)

26
Q

k(AB) =

A

(kA)B = A(kB)

27
Q

(a + b)C =

A

aC + bC

28
Q

(ab) C =

A

b(aC) = a(bC)

29
Q

What is the identity matrix?

A

square matrix (size depending on the other matrices in the equation) where all its entries are 0 and the main diagonal entries are 1

30
Q

A*A^-1 =

A

I

31
Q

How do you find determinant of 2x2 matrix?

det(a) or IAI

A

ad–bc

32
Q

How do you find inverse of 2x2 matrix?

A

A^ -1 = 1/det(A) [exchange a with d; exchange signs of b and c]

33
Q

A^n =

A

A multiplied n number of times

34
Q

A^0 =

A

I subscript matrix size

35
Q

A^n * A^r =

A

A^(n+r)

36
Q

(A^n)^r =

A

A ^ (n*r)

37
Q

A^ -n =

A

(A^-1)^n = (A^n)^-1

38
Q

(A^-1)^-1 =

(A^T)^T =

A

A

39
Q

(A^-1)^n =

(A^T)^-1 =

A

(A^n)^-1

(A^-1)^T

40
Q

(A+B)^-1 =

(A+B)^T =

A

(A^-1 + B^-1)

(A^T + B^T)

41
Q

(k*A)^-1 =

(k*A)^T =

A

k^-1 * A^-1 = (1/k) * A^-1

k * A^T

42
Q

(ABCD)^-1 =

(ABCD)^T =

A

D^-1 * C^-1 * B^-1 * A^-1

D^T * C^T * B^T * A^T

43
Q

How do you find A in AX=b?

A

X=A^-1 * b

44
Q

What is a homogenous system?

A

solutions are = 0

45
Q

What is a diagonal matrix?

A

All entries beyond the main diagonal are 0 in a square matrix

46
Q

What are the 2 properties of the diagonal matrix?

A

1 ) the diagonal matrix is invertible if none of its main diagonal entries is 0
2 ) the power of the matrix can be distributed to the entries of the main diagonal

47
Q

What does the LOWER triangular matrix look like?

A

entries above main diagonal are 0

48
Q

What does the UPPER triangular matrix look like?

A

entries below main diagonal are 0

49
Q

If any entry of the main diagonal of the triangular matrix is 0:

A

it is SINGULAR

50
Q

SINGULAR =

A

NOT INVERTIBLE

51
Q

The main diagonal of a symmetric matrix acts as a _______

A

mirror line

52
Q

The transpose of the symmetrical matrix is _______ to original matrix

A

identical

53
Q

The inverse, if it exists, of the symmetrical matrix is _______ to original matrix

A

identical

54
Q

The inverse of a matrix only exists if:

A

det(A) does not = 0

Linear Algebra (1 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions