Linear Algebra Exam 2026 Questions and Answers Graded A+

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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