Linear Algebra Exam 2026 Questions and
Answers Graded A+
Echelon Form - Correct answer-1. All nonzero rows are above any rows of all
zeros.
2. Each leading entry of a row is in a column to the right of the leading entry of the
row above it.
3. All entries in a column below a leading entry are zeros.
augmented matrix - Correct answer-A matrix that consists of the coefficients and
the constant terms in a system of linear equations.
Homogeneous Linear System - Correct answer-A linear system of the form Ax=0.
This type of system cannot be inconsistent
linear combination - Correct answer-If u₁,u₂,...,u_m are vectors and c₁,c₂,..,c_m are
scalars, then
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, c₁u₁+c₂u₂+...+c_m*u_m
is a _________________- of the vectors.
span - Correct answer-The ___________ of a set of vectors [u_1,u_2...] is the set
of all linear combinations x_1u_1+x_2u_2+...+x_mu_m
where [u_1,u_2,...,u_m] is the set
If v is in the span of [u_1,u_2...], then v=x_1u_1+x_2u_2+...+x_mu_m for some
values of the x's.
linearly independent - Correct answer-an indexed set {v1, ..., vp} with the property
that the vector equation c1v1 + c2v2 + ... + cnvn = 0 has only the trivial solution
If a set of vectors form a matrix whose determinant is non-zero, then the vectors
are linearly independent.
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Answers Graded A+
Echelon Form - Correct answer-1. All nonzero rows are above any rows of all
zeros.
2. Each leading entry of a row is in a column to the right of the leading entry of the
row above it.
3. All entries in a column below a leading entry are zeros.
augmented matrix - Correct answer-A matrix that consists of the coefficients and
the constant terms in a system of linear equations.
Homogeneous Linear System - Correct answer-A linear system of the form Ax=0.
This type of system cannot be inconsistent
linear combination - Correct answer-If u₁,u₂,...,u_m are vectors and c₁,c₂,..,c_m are
scalars, then
©COPYRIGHT 2025,ALL RIGHTS RESERVED 1
, c₁u₁+c₂u₂+...+c_m*u_m
is a _________________- of the vectors.
span - Correct answer-The ___________ of a set of vectors [u_1,u_2...] is the set
of all linear combinations x_1u_1+x_2u_2+...+x_mu_m
where [u_1,u_2,...,u_m] is the set
If v is in the span of [u_1,u_2...], then v=x_1u_1+x_2u_2+...+x_mu_m for some
values of the x's.
linearly independent - Correct answer-an indexed set {v1, ..., vp} with the property
that the vector equation c1v1 + c2v2 + ... + cnvn = 0 has only the trivial solution
If a set of vectors form a matrix whose determinant is non-zero, then the vectors
are linearly independent.
©COPYRIGHT 2025,ALL RIGHTS RESERVED 2
