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20 Cards in this Set

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If the system has fewer eqns than variables,
then it must have an infinite number of solns
if a matrix possesses an inverse,
then the inverse is unique. Inverse of A is A^-1
Because the system have the same coeff matrix
one could join the two non-coeff column matrices together
If the system has fewer eqns than variables,
then it must have an infinite number of solns
the sum of two matrices of diff sizes is
undefined, b/c the # of columns must be equal to the # of rows in the 2nd matrix
Singular matrix results
in a row of zeros, which makes it impossible to rewrite into [I|A^-1]
what is a symmetric matrix
square matrix that is equal to its transpose matrix

(A^T)^T
formula for inverse of A matrix is
A^-1 =1/ad-bc[d -b]
[-c a] if det is not equal to zero
(AB)^-1
A^-1 *B^-1
if c is invertible, then cancellation rule applies
1. if AC=BC, then A=B
2. if CA=CB, then A=B
if A is an invertible matrix, the sys of eqns Ax=b has a unique soln given by
x=A^-1b
two eqns are called parallel
if the left side of one eqn is a multiple of the other and inconsistent
polynomial in one variable of degree 2 is called
p(x) = a0 + a1x + a^2*x^2
y=a0+a1x+a2x2
det(AB)
det(A)*det(B)
An nxn matrix is invertible<->
determinant is not equal to zero
prove by induction
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
an nxn matrix is called elementary matrix if it can be obtained from the identity matrix by
a single elementary row operation and it needs to be a square matrix
every elementary matrix is
invertible and the inverse of an elementary matrix is another elementary mateix
a square matrix A is invertible<->
it can be written as the product of elementary matrices
a square matrix A is invertible<->
it can be written as the product of elementary matrices