Exam (elaborations)
Math 218 - Matrices Quiz 1 Questions And Answers Latest Update
- Course
- Math 218
- Institution
- Duke University
Math 218 - Matrices Quiz 1 Questions And Answers Latest Update
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Solution 2024/2025Pepper
Math 218 - Matrices Quiz 1 Questions And
Answers Latest Update
A matrix is in the row echelon form if ANS✔✔ in any two consecutive rows,
the pivot in the row below is to the right of the pivot in the row above. and
any row of zeros is at the end of the matrix.
A matrix is in the reduced row echelon form if ANS✔✔ it is in r.e.f, the pivots
are 1, and the rest of the entries are 0
A linear system is inconsistent if it admits ANS✔✔ no solution
A linear system is consistent if it admits ANS✔✔ a unique solution or
infinitely many solutions
what are elementary row operations? ANS✔✔ 1. Swap two rows
2. Multiply each element in a row or column by a non-zero value.
3. Multiply a row by a nonzero numb and add result to another row.
How to get solution of system using augmented matrix ANS✔✔ perform row
operations to reach r.e.f and get equations. Or do r.r.e.f and get solution on
the right
A linear system whose equations are all homogeneous must be consistent
ANS✔✔ True
, Solution 2024/2025
Pepper
A single linear equation with two or more unknowns must have inf many
solutions. ANS✔✔ true
A system has 3 equations (3 pivots) and 4 variables, what are possible
solutions? ANS✔✔ infinitely many or no solution
if m >= n ANS✔✔ unique, infinitely many or no solution
if m<n ANS✔✔ infinitely many or no solution
when does system have a unique solution? ANS✔✔ pivot = num of variables
It is possible to get different r.e.f for the same matrix ANS✔✔ true, r.e.f is
not unique but r.r.e.f and solution is
What is a homogeneous system? ANS✔✔ all the constants are = 0
What is a property of homogeneous system? ANS✔✔ Always consistent
since the trivial solution is always a solution
if m<n and homogeneous then ANS✔✔ system has infinitely many solutions
row vector ANS✔✔ 1xn matrix
column vector ANS✔✔ a matrix with only one column (mx1)
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