Matrix Theory Quiz

Which of the following is true about a matrix in echelon form?

• A) All elements are 0

• B) All leading entries are 1

• C) All zero rows are at the bottom

• D) Each row is linearly independent

In row echelon form, the leading entry in each nonzero row must:

• A) Be zero

• B) Be to the right of the leading entry above

• C) Be to the left of the previous pivot

• D) Be negative

A matrix is in row echelon form if:

• A) Every column has a pivot

• B) Leading entries can be anywhere

• C) Zeros below pivots exist

• D) Zeros are only at the top

The pivot positions in echelon form refer to:

• A) The largest numbers

• B) Entries equal to zero

• C) The first non-zero entry in each row

• D) Diagonal entries only

Which is not a requirement for echelon form?

• A) Zeros below each pivot

• B) Leading 1s in each row

• C) Zero rows at the bottom

• D) Pivot columns ordered left to right

In reduced row echelon form (RREF), each leading 1 must:

• A) Be below all zeros

• B) Be the only non-zero in its column

• C) Appear in the same column

• D) Not exist

RREF requires the leading 1s to:

• A) Move left to right in each column

• B) Appear randomly

• C) Be only in the diagonal

• D) Be to the right of the leading 1 in the row above

RREF is different from REF because:

• A) It contains zero rows

• B) Pivots are non-zero

• C) It forces zeroes above and below each pivot

• D) It uses only 2 rows

Can every matrix be reduced to RREF using row operations?

• A) Yes

• B) No

• C) Only square ones

• D) Only identity matrices

A row of all zeros appears:

• A) At the top

• B) In the middle

• C) At the bottom

• D) In diagonal