Math 10.1

Front 1

If the system has fewer eqns than variables,

Back 1

then it must have an infinite number of solns

Front 2

if a matrix possesses an inverse,

Back 2

then the inverse is unique. Inverse of A is A^-1

Front 3

Because the system have the same coeff matrix

Back 3

one could join the two non-coeff column matrices together

Front 4

If the system has fewer eqns than variables,

Back 4

then it must have an infinite number of solns

Front 5

the sum of two matrices of diff sizes is

Back 5

undefined, b/c the # of columns must be equal to the # of rows in the 2nd matrix

Front 6

Singular matrix results

Back 6

in a row of zeros, which makes it impossible to rewrite into [I|A^-1]

Front 7

what is a symmetric matrix

Back 7

square matrix that is equal to its transpose matrix

(A^T)^T

Front 8

formula for inverse of A matrix is

Back 8

A^-1 =1/ad-bc[d -b]
[-c a] if det is not equal to zero

Front 9

(AB)^-1

Back 9

A^-1 *B^-1

Front 10

if c is invertible, then cancellation rule applies

Back 10

1. if AC=BC, then A=B
2. if CA=CB, then A=B

Front 11

if A is an invertible matrix, the sys of eqns Ax=b has a unique soln given by

Back 11

x=A^-1b

Front 12

two eqns are called parallel

Back 12

if the left side of one eqn is a multiple of the other and inconsistent

Front 13

polynomial in one variable of degree 2 is called

Back 13

p(x) = a0 + a1x + a^2*x^2
y=a0+a1x+a2x2

Front 14

det(AB)

Back 14

det(A)*det(B)

Front 15

An nxn matrix is invertible<->

Back 15

determinant is not equal to zero

Front 16

prove by induction

Back 16

statemts s1,s2,s3,...Sn
-show S1 is true
-show if Sn holds, then so does next one(Sn+1)
-Conclusion:Sn is true for al n

Front 17

an nxn matrix is called elementary matrix if it can be obtained from the identity matrix by

Back 17

a single elementary row operation and it needs to be a square matrix

Front 18

every elementary matrix is

Back 18

invertible and the inverse of an elementary matrix is another elementary mateix

Front 19

a square matrix A is invertible<->

Back 19

it can be written as the product of elementary matrices

Front 20

a square matrix A is invertible<->

Back 20

it can be written as the product of elementary matrices