Question

Determine if the columns of the matrix form a linearly independent set. 1 2-3 1 2 5 - 4 -2 - 14 2 7 2 Select the correct choice below and fill in the answer box to complete your choice. A. The columns are not linearly independent because the reduced row echelon form of is A 0 B. The columns are linearly independent because the reduced row echelon form ofA 0 is

Answer 1

A = [1 2 12 2 5 -3 17 -4 -21 F 2 -14 ] Consider the augmented matrix [A : 0] T 2 -3 1 107 12 5 -4 -2 10 12 7 2 - 14101 Convert it to its reduced row echelon yon Tt 2 -3 1107 Ra + R2-2hi lo Rg Å3-2R, 10 I 2 3 8 -4/ol -160l It I R3 R3 - 3 Rg lo 1 10 lo 2 -3 1107 I 2-4 ol o 2-410 2 -3 1107 1 2 -410 o 1-2lol I Rgt / Raz

.:. The reduced row echelon form of [Aio] lo lo 7 0 2 1 -4 10 - 2 Only three columns have pivot element (shown in boses). o Columns of a fo matris form a linearly independent set if all columns have pivot element. Here 4th column doesnot have pivot. & The columns are NOT linearly independent : (A) ✓