LINEAR ALGEBRA EXAM GUIDE 2
QUESTIONS AND ANSWERS
Reduced Echelon Form - Answer-The leading entry in each nonzero row is 1 and each
leading 1 is the only nonzero entry in its column
row Echelon form - Answer-the leading entry in each nonzero row is 1 but there can be
numbers other than 1 above the diagonal
Homogeneous Systems - Answer-linear system on the right-hand side are all zero;
every homogeneous linear system either has only solution or infinitely many solution
what is a linear combination? - Answer-c1v1+c2v2+cnvn= [x,yz] or [0,0,0]
what’s the solution to a homogeneous linear system with more variables than equations
- Answer-infinitely many solutions.
what's the solution to a homogeneous system with coefficient matrix A if A is row
equivalent to the identity matrix. - Answer-one solution
in homogenous system which columns have leading variables or are free variables? -
Answer-X1,X2 - leading variables
X3,X4 - free variables(s,t)
how do you find the product of matrices? - Answer-sum of products
what is the cancellation rule? - Answer-ad=ac and a /= 0, b = c
ad = 0, a = 0 or d =0
how do you know if matrices are inversions of each other? - Answer-if A*B = I =B*A
how do you know a 2x2 matrix is invertible? - Answer-if ad -bc /= 0
what is the formula for the inverse of a 2x2 matrix? - Answer-1/ad-bc[d -b;-c a]
if the n*n matrix is invertible for any vector in b, then Ax = b. how do you solve for x? -
Answer-x = A^-1*b
how do you know when a n*n matrix is invertible? - Answer--if its rref = i matrix
-det /=0
-if Ax= b has a unique solution for any vetor b
-if Ax= 0 has only one solution x = 0
QUESTIONS AND ANSWERS
Reduced Echelon Form - Answer-The leading entry in each nonzero row is 1 and each
leading 1 is the only nonzero entry in its column
row Echelon form - Answer-the leading entry in each nonzero row is 1 but there can be
numbers other than 1 above the diagonal
Homogeneous Systems - Answer-linear system on the right-hand side are all zero;
every homogeneous linear system either has only solution or infinitely many solution
what is a linear combination? - Answer-c1v1+c2v2+cnvn= [x,yz] or [0,0,0]
what’s the solution to a homogeneous linear system with more variables than equations
- Answer-infinitely many solutions.
what's the solution to a homogeneous system with coefficient matrix A if A is row
equivalent to the identity matrix. - Answer-one solution
in homogenous system which columns have leading variables or are free variables? -
Answer-X1,X2 - leading variables
X3,X4 - free variables(s,t)
how do you find the product of matrices? - Answer-sum of products
what is the cancellation rule? - Answer-ad=ac and a /= 0, b = c
ad = 0, a = 0 or d =0
how do you know if matrices are inversions of each other? - Answer-if A*B = I =B*A
how do you know a 2x2 matrix is invertible? - Answer-if ad -bc /= 0
what is the formula for the inverse of a 2x2 matrix? - Answer-1/ad-bc[d -b;-c a]
if the n*n matrix is invertible for any vector in b, then Ax = b. how do you solve for x? -
Answer-x = A^-1*b
how do you know when a n*n matrix is invertible? - Answer--if its rref = i matrix
-det /=0
-if Ax= b has a unique solution for any vetor b
-if Ax= 0 has only one solution x = 0
