Question

Determine if b is a linear combination of a1, a2, and a3. $mathbf{a}_1 = egin{bmatrix} 1 -3 0 end{bmatrix}$, $mathbf{a}_2 = egin{bmatrix} 0 1 2 end{bmatrix}$, $mathbf{a}_3 = egin{bmatrix} 6 -6 24 end{bmatrix}$, $mathbf{b} = egin{bmatrix} 2 -3 6 end{bmatrix}$ Choose the correct answer below. A. Vector b is not a linear combination of a1, a2, and a3. B. Vector b is a linear combination of a1, a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the fourth column. C. Vector b is a linear combination of a1, a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the third column. D. Vector b is a linear combination of a1, a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column and the second entry in the second column.

          Determine if b is a linear combination of a1, a2, and a3.
$mathbf{a}_1 = egin{bmatrix} 1  -3  0 end{bmatrix}$,  $mathbf{a}_2 = egin{bmatrix} 0  1  2 end{bmatrix}$,  $mathbf{a}_3 = egin{bmatrix} 6  -6  24 end{bmatrix}$,  $mathbf{b} = egin{bmatrix} 2  -3  6 end{bmatrix}$
Choose the correct answer below.
A. Vector b is not a linear combination of a1, a2, and a3.
B. Vector b is a linear combination of a1, a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the fourth column.
C. Vector b is a linear combination of a1, a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the third column.
D. Vector b is a linear combination of a1, a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column and the second entry in the second column.

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Determine if b is a linear combination of a1, a2, and a3.
mathbfa1 = eginbmatrix 1 -3 0 endbmatrix, mathbfa2 = eginbmatrix 0 1 2 endbmatrix, mathbfa3 = eginbmatrix 6 -6 24 endbmatrix, mathbfb = eginbmatrix 2 -3 6 endbmatrix
Choose the correct answer below.
A. Vector b is not a linear combination of a1, a2, and a3.
B. Vector b is a linear combination of a1, a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the fourth column.
C. Vector b is a linear combination of a1, a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the third column.
D. Vector b is a linear combination of a1, a2, and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column and the second entry in the second column.

Added by Bethany H.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert David Mccaslin

Step 1

To determine if \(\mathbf{b}\) is a linear combination of \(\mathbf{a}_1\), \(\mathbf{a}_2\), and \(\mathbf{a}_3\), we need to solve the equation \(c_1 \mathbf{a}_1 + c_2 \mathbf{a}_2 + c_3 \mathbf{a}_3 = \mathbf{b}\) for scalars \(c_1\), \(c_2\), and \(c_3\). Show more…

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Determine if a linear combination. Choose the correct answer below: Vector linear combination of a1 and a3. The pivots in the corresponding echelon matrix are the first entry in the first column, the second entry in the second column, and the third entry in the fourth column. Linear combination of 01 and 83. The pivots in the corresponding echelon matrix are the first entry in the first column, the second entry in the second column, and the third entry in the third column. Linear combination of a1, a2, and a3. The pivots in the corresponding echelon matrix are the first entry in the first column and the second entry in the second column. Vector Vector

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