Question

For each of the following matrices determine whether the matrix is in REF, in RREF or in neither RREF nor REF 0 2 -1 34 010 3 0 B- 00 2-5 0 A-0 0 0 0 0 000 0 1 0 0 0 2 1 0 1 0-4 0 D=100 C-1001 000 0 1 14-17 0 0-2 6 3 00 0 1 4 00 0 0 -3 0 0 1 G- 10 H=1000 0 0 1 J-0 0 1 A Choose... Choose... K RREF but not REF REF but not RREF H RREF Not RREF and not REF F Choose... Choose .. J Choose C Choose.. B Choose... E Choose... G Choose...

Answer 1

A matrix is said to be in row echelon form (REF) if it satisfies the following 3 conditions:

i. All nonzero rows are above the zero rows, if any.

ii. Each non-zero leading entry of a row is in a column to the right of the non-zero leading entry of the row above it.

iii. All entries in a column below a non-zero leading entry are zeros.

A matrix, if in its REF, is said to be in its reduced row echelon form (RREF), if it satisfies the following 2 conditions:

1. The leading non-zero entry in each row is 1.

2. Each leading 1 is the only non-zero entry in its column.

A. The matrix is not RREF and, not REF.

B. REF but not RREF .

C. RREF.

D. The matrix is not RREF and, not REF.

E. REF.

F. RREF.

G. The matrix is not RREF and, not REF.

H. RREF.

J. RREF.

K. RREF.