Term Test 2

Question 1

Transpose of a matrix, A^T

Answer 1

the rows and columns are switched

Question 2

Invertibility or non singularity

Answer 2

A matrix A is invertible is there is a matrix B such that AB=In=BA. A^-1

Question 3

Determinant

Answer 3

ad-bc

Question 4

When is a matrix invertible

Answer 4

when det(A) does not equal 0

Question 5

Elementary matrices

Answer 5

found by altering the nxn identity matrix

1. interchanging two rows
2. one row of In is multiplied by a scalar
3. adding a multiple of one row of In to another row of In

Question 6

Subspace of a vector space V in any set H

Answer 6

1. the zero vector is in H
2. closed under vector addition
3. closed under scalar multiplication

Question 7

null space of matrix A [nul(A)]

Answer 7

set of all solutions to the homogenous eq ax=0

Question 8

column space of matrix A [col(A)]

Answer 8

set of all lin combos of the columns of A

Question 9

basis

Answer 9

a lin indep set of vectors that spans subspace H is the basis of H

Question 10

dimension of vector space V [dim(V)]

Answer 10

the number of vectors in a basis of V

Question 11

rank of matrix A [rank(A)]

Answer 11

is equal to the dimension of col(A)

Question 12

nullity of a matrix A [nullity(A)]

Answer 12

is equal to the dimension of nul(A)

Question 13

minor of aij (aka Mij)

Answer 13

the (n-1)x(n-1) matrix obtained by deleting the ith row and jth column of matrix A