Detemine if b is a linear combination of a1,a2,a3 a1=[202],a2=[−43−4],a3=[−584],b=[13−49] Choose the correct answer below A. Vector b is a linear combination of a1,a2,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. B. Vector b is not a lincar combination of a1,a2,a3 C. Vector b is a linear combination of a1,a2,a3. The pivots in the corresponding echelon matrix are in the first entry in the first column and the third entry in the second column, and the third entry in the third column. D. Vector b is a linear combination of a1,a2,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.

Question

Detemine if b is a linear combination of a1,a2,a3  a1=[202],a2=[−43−4],a3=[−584],b=[13−49]  Choose the correct answer below  A. Vector b is a linear combination of a1,a2,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.  B. Vector b is not a lincar combination of a1,a2,a3  C. Vector b is a linear combination of a1,a2,a3. The pivots in the corresponding echelon matrix are in the first entry in the first column and the third entry in the second column, and the third entry in the third column.  D. Vector b is a linear combination of a1,a2,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.

Chanell Sanborn · Accepted Answer

Consider the following vectors:  a1=[202],a2=[−43−4],a3=[−584],b=[13−49]  First, check whether the vector b is in linear combination of the other three vectors or not.  [13−49]=c1[202]+c2=[−43−4]+c3[−584]  =[2c1−4c2−5c33c2+8c32c1−4c2+4c3]  The followng equations can be expressed in matrix form as follows:  =[2−4−513038−42−449]  Apply R3⇒R3−R1  =[2−4−513038−40099]  Apply R2⇒13R2  =[2−4−5130183−430099]  Apply R1⇒12R1  =[1−2−521320183−430099]  Since, every row has a pivot position there extra a unique solution to the system.  Hence there is a solution to the system [13−49]=[2c1−4c2−5c33c2+8c32c1−4c2+4c3].  Clearly, the pivot positions are in the first entry in the first column, second entry n the second column, and the third entry in the third column as shown below:

Jeffery Autrey · Accepted Answer

Great, thanks a lot!

Detemine if b is a linear combination of a_1, a_2,

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