ol.lst-kix_8a2cgdfowtn1-8.start{counter-reset:lst-ctn-kix_8a2cgdfowtn1-8 0}ol.lst-kix_8a2cgdfowtn1-3.start{counter-reset:lst-ctn-kix_8a2cgdfowtn1-3 0}.lst-kix_8a2cgdfowtn1-3 > li{counter-increment:lst-ctn-kix_8a2cgdfowtn1-3}ol.lst-kix_8a2cgdfowtn1-1.start{counter-reset:lst-ctn-kix_8a2cgdfowtn1-1 0}.lst-kix_8a2cgdfowtn1-0 > li{counter-increment:lst-ctn-kix_8a2cgdfowtn1-0}.lst-kix_8a2cgdfowtn1-4 > li{counter-increment:lst-ctn-kix_8a2cgdfowtn1-4}.lst-kix_8a2cgdfowtn1-8 > li:before{content:"" counter(lst-ctn-kix_8a2cgdfowtn1-8,lower-roman) ". "}.lst-kix_8a2cgdfowtn1-7 > li:before{content:"" counter(lst-ctn-kix_8a2cgdfowtn1-7,lower-latin) ". "}.lst-kix_8a2cgdfowtn1-6 > li:before{content:"" counter(lst-ctn-kix_8a2cgdfowtn1-6,decimal) ". "}.lst-kix_8a2cgdfowtn1-7 > li{counter-increment:lst-ctn-kix_8a2cgdfowtn1-7}ol.lst-kix_8a2cgdfowtn1-4{list-style-type:none}ol.lst-kix_8a2cgdfowtn1-3{list-style-type:none}ol.lst-kix_8a2cgdfowtn1-6{list-style-type:none}ol.lst-kix_8a2cgdfowtn1-5{list-style-type:none}ol.lst-kix_8a2cgdfowtn1-6.start{counter-reset:lst-ctn-kix_8a2cgdfowtn1-6 0}ol.lst-kix_8a2cgdfowtn1-0{list-style-type:none}ol.lst-kix_8a2cgdfowtn1-2{list-style-type:none}ol.lst-kix_8a2cgdfowtn1-1{list-style-type:none}.lst-kix_8a2cgdfowtn1-1 > li{counter-increment:lst-ctn-kix_8a2cgdfowtn1-1}.lst-kix_8a2cgdfowtn1-0 > li:before{content:"" counter(lst-ctn-kix_8a2cgdfowtn1-0,decimal) ". "}.lst-kix_8a2cgdfowtn1-1 > li:before{content:"" counter(lst-ctn-kix_8a2cgdfowtn1-1,lower-latin) ". "}.lst-kix_8a2cgdfowtn1-2 > li:before{content:"" counter(lst-ctn-kix_8a2cgdfowtn1-2,lower-roman) ". "}ol.lst-kix_8a2cgdfowtn1-8{list-style-type:none}ol.lst-kix_8a2cgdfowtn1-7{list-style-type:none}.lst-kix_8a2cgdfowtn1-4 > li:before{content:"" counter(lst-ctn-kix_8a2cgdfowtn1-4,lower-latin) ". "}.lst-kix_8a2cgdfowtn1-8 > li{counter-increment:lst-ctn-kix_8a2cgdfowtn1-8}.lst-kix_8a2cgdfowtn1-3 > li:before{content:"" counter(lst-ctn-kix_8a2cgdfowtn1-3,decimal) ". "}.lst-kix_8a2cgdfowtn1-5 > li:before{content:"" counter(lst-ctn-kix_8a2cgdfowtn1-5,lower-roman) ". "}.lst-kix_8a2cgdfowtn1-2 > li{counter-increment:lst-ctn-kix_8a2cgdfowtn1-2}ol.lst-kix_8a2cgdfowtn1-4.start{counter-reset:lst-ctn-kix_8a2cgdfowtn1-4 0}ol.lst-kix_8a2cgdfowtn1-0.start{counter-reset:lst-ctn-kix_8a2cgdfowtn1-0 0}.lst-kix_8a2cgdfowtn1-5 > li{counter-increment:lst-ctn-kix_8a2cgdfowtn1-5}ol.lst-kix_8a2cgdfowtn1-5.start{counter-reset:lst-ctn-kix_8a2cgdfowtn1-5 0}ol.lst-kix_8a2cgdfowtn1-7.start{counter-reset:lst-ctn-kix_8a2cgdfowtn1-7 0}.lst-kix_8a2cgdfowtn1-6 > li{counter-increment:lst-ctn-kix_8a2cgdfowtn1-6}ol.lst-kix_8a2cgdfowtn1-2.start{counter-reset:lst-ctn-kix_8a2cgdfowtn1-2 0}

Analysis Final Exam Study GuideWe also discuss several other topics like What happen when a person has insulin resistance?

Chapter 7: Matrix addition and scalar multiplication:

Don't forget about the age old question of What is a germ-line cell?

# rows X # columns

Matrix additionDon't forget about the age old question of What are the ways and means of a committee dealing with finance?

                Need to be equal sizeWe also discuss several other topics like What are the rights of general partners?
We also discuss several other topics like What are the sources of information in measuring performance?

Matrix multiplicationWe also discuss several other topics like How do kidneys regulate blood pressure and blood volume?

Ex:

Transpose of a matrix

Section 7.3 Linear Algebra: matrices, vectors and linear systems of equations

Section 7.4 Linear independence and rank of a matrix and vector spaces

Rank

Ex: Determine the rank:

Linear Independence

Ex: Consider (1,-1,1),(0,1,1),(1,1,1) and determine if they are linearly independent

Rank = 3. Linearly independent since rank > # of vectors

Section 7.5: Solutions of Linear Systems

Theorem

1. Existence: system has solutions if the coefficient matrix A and its augmented matrix à have the same rank
2. Uniqueness: 1 solution if A= Ã = n
3. If rank < n ⇾ infinite solutions
4. Solution obtained by gauss elimination

Ex: use the rank to identity if there is a solution solve

Section 7.7: Determinant of a matrix:

Ex: Find D(A):

Section 7.8 inverse of a matrix and Gauss-Jordan elimination:

Matrix inverse:

        A=A-1

        A.A-1=1

Ex: find A-1 of A and demonstrate it is correct:

Cramer’s Rule:

For 2x2 systems:

For 3x3 systems:

References: