Math 225 Exam #1 Exam Questions And
Answers Latest 2025
Augmented matrix -
correct answer ✅a+b=c
d+e=f
[ a b c ; d e f]
Row echelon form (REF) -
correct answer ✅1. All nonzero rows are above any rows of all
zeros, called 0-rows
2. Each leading entry (leftmost nonzero entry) of a row is in a
column to the right of the leading entry of the row above it
3. All entires in a column below a leading entry are zero
Reduced row echelon form -
correct answer ✅All the rules for row echelon for plus...
1. The leading entry in each nonzero row is 1
2. Each leading 1 is the only nonzero entry in its column
General solution of a SLE in parametric vector form -
correct answer ✅-set free variables equal to s and t
-set up constant matrix, s matrix, and t matrix
ex.
, Math 225 Exam #1 Exam Questions And
Answers Latest 2025
x1-x4=-1
x2+x3+2x4=2
x3=s
x4=t
x1=t-1
x2=2-s-2t
[x1 ; x2 ; x3 ; x4]= [-1 ; 2 ; 0 ; 0] + s*[0 ; -1 ; 1 ; 0] + t*[1 ; -2 ; 0 ; 1]
Span of vectors in Rn -
correct answer ✅The Span{v1, v2, ..., vp} is the set of all linear
combinations of vectors v1, v2, ..., vp. In other words, Span{v1,
v2, ..., vp} is the collection of all vectors that can be written in the
form x1v1 + x2v2 + ... + xpvp where x1, x2, ..., xp are all scalars
Linearly independent -
correct answer ✅a set of vectors {v1, v2, ..., vp} in Rn where the
vector equation x1v1 + x2v2 + ... + xpvp = 0 has only the trivial
solution (x1=0, x2=0, & xp=0)
Linearly dependent -
correct answer ✅a set of vectors {v1, v2, ..., vp} in Rn where there
Answers Latest 2025
Augmented matrix -
correct answer ✅a+b=c
d+e=f
[ a b c ; d e f]
Row echelon form (REF) -
correct answer ✅1. All nonzero rows are above any rows of all
zeros, called 0-rows
2. Each leading entry (leftmost nonzero entry) of a row is in a
column to the right of the leading entry of the row above it
3. All entires in a column below a leading entry are zero
Reduced row echelon form -
correct answer ✅All the rules for row echelon for plus...
1. The leading entry in each nonzero row is 1
2. Each leading 1 is the only nonzero entry in its column
General solution of a SLE in parametric vector form -
correct answer ✅-set free variables equal to s and t
-set up constant matrix, s matrix, and t matrix
ex.
, Math 225 Exam #1 Exam Questions And
Answers Latest 2025
x1-x4=-1
x2+x3+2x4=2
x3=s
x4=t
x1=t-1
x2=2-s-2t
[x1 ; x2 ; x3 ; x4]= [-1 ; 2 ; 0 ; 0] + s*[0 ; -1 ; 1 ; 0] + t*[1 ; -2 ; 0 ; 1]
Span of vectors in Rn -
correct answer ✅The Span{v1, v2, ..., vp} is the set of all linear
combinations of vectors v1, v2, ..., vp. In other words, Span{v1,
v2, ..., vp} is the collection of all vectors that can be written in the
form x1v1 + x2v2 + ... + xpvp where x1, x2, ..., xp are all scalars
Linearly independent -
correct answer ✅a set of vectors {v1, v2, ..., vp} in Rn where the
vector equation x1v1 + x2v2 + ... + xpvp = 0 has only the trivial
solution (x1=0, x2=0, & xp=0)
Linearly dependent -
correct answer ✅a set of vectors {v1, v2, ..., vp} in Rn where there
