Determine if b is a linear combination of a1, a2, and a 4 12 Choose the correct

Question

Determine if b is a linear combination of a1, a2, and a 4 12 Choose the correct answer below OA. Vector b is a linear combination of a, a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the ? B. Vector b is a linear combination of al a2 and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the ? C Vector b ls a near combination of a a2 and a3 The pvos in the corresponding echelon matrix are in the first entry In the first column and the second entry in OD. Vector b is not a linear combination of a1, a2, and a3. second column, and the third entry in the third column. second column, and the third entry in the fourth column. the second columrn

Explanation / Answer

augmented matrix for the system is

convert into  Reduced Row Eschelon Form...

Add (3 * row1) to row2

Add (-4 * row2) to row3

here last row is zero so

Vector b is a linear combination of a1, a2, a3 . The pivot in the corresponding echelon matrix are in the first entry in the first column and the second entry in the second column

Option C is correct

1 0 5 2 -3 1 -4 -3 0 4 44 12

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