MATH 2318: LINEAR ALGEBRA EXAM 1
QUESTIONS AND ANSWERS
what is the relationship between pivots and free vs. basic variables? - Answer-- has a
pivot = basic variable
- no pivot = free variable
row-echelon form (REF) - Answer-1. any row consisting of only zeros must be at the
bottom
2. for each row not entirely of zeros, 1st nonzero interty is 1 (leading 1)
3. for tow consecutive rows, leading 1 in higher row must be more left than leading 1 in
lower row
Reduced Row Echelon Form (RREF) - Answer-when every column that has a leading 1
has zeros in every position above and below its leading 1
rules for pivots - Answer-1. a row or column can ONLY contain at most 1 pivot
2. pivot remains unchanged in elimination step
3. no more pivot = process stops
homogenous vs. Non homogenous - Answer-- homo = equation equals to zero
- non homo = equations does not equal zero
row equivalent matrices - Answer-Two matrices for which there exists a (finite)
sequence of row operations that transforms one matrix into the other.
what are the number of solutions of a homogenous system? - Answer-if there are less
equations than variables, then system has infinite number of solutions
Diagonal matrix - Answer-a square matrix whose entries not on the main diagonal are
all zero
trace of the matrix - Answer-sum of diagonal entries
identity matrix - Answer-square matrix whose diagonal elements are all 1's
size importance in adding/subtracting matrices - Answer-the two matrices MUST be the
same size
size importance in multiplying matrices - Answer-- the number of columns of the first
matrix MUST equal the number of rows of the second matrix
- the end size is: # of rows of 1st matrix x # of columns of 2nd matric
linear combination - Answer-- A = coefficient matrix
QUESTIONS AND ANSWERS
what is the relationship between pivots and free vs. basic variables? - Answer-- has a
pivot = basic variable
- no pivot = free variable
row-echelon form (REF) - Answer-1. any row consisting of only zeros must be at the
bottom
2. for each row not entirely of zeros, 1st nonzero interty is 1 (leading 1)
3. for tow consecutive rows, leading 1 in higher row must be more left than leading 1 in
lower row
Reduced Row Echelon Form (RREF) - Answer-when every column that has a leading 1
has zeros in every position above and below its leading 1
rules for pivots - Answer-1. a row or column can ONLY contain at most 1 pivot
2. pivot remains unchanged in elimination step
3. no more pivot = process stops
homogenous vs. Non homogenous - Answer-- homo = equation equals to zero
- non homo = equations does not equal zero
row equivalent matrices - Answer-Two matrices for which there exists a (finite)
sequence of row operations that transforms one matrix into the other.
what are the number of solutions of a homogenous system? - Answer-if there are less
equations than variables, then system has infinite number of solutions
Diagonal matrix - Answer-a square matrix whose entries not on the main diagonal are
all zero
trace of the matrix - Answer-sum of diagonal entries
identity matrix - Answer-square matrix whose diagonal elements are all 1's
size importance in adding/subtracting matrices - Answer-the two matrices MUST be the
same size
size importance in multiplying matrices - Answer-- the number of columns of the first
matrix MUST equal the number of rows of the second matrix
- the end size is: # of rows of 1st matrix x # of columns of 2nd matric
linear combination - Answer-- A = coefficient matrix
