Homework SourseLet matrices bA1A2A3 be given by b1 0 2 A13 2 4 A24 3 3 A31
Let matrices b,A1,A2,A3 be given by b=[1 0 -2]
A1=[3 2 4] A2=[4 3 3] A3=[1 0 -1]
Verify whether or not the matrix b is a linear combination of the matrices A1, A2, and A3
Let matrices b,A1,A2,A3 be given by b=[1 0 -2]
A1=[3 2 4] A2=[4 3 3] A3=[1 0 -1]
Verify whether or not the matrix b is a linear combination of the matrices A1, A2, and A3
A1=[3 2 4] A2=[4 3 3] A3=[1 0 -1]
Verify whether or not the matrix b is a linear combination of the matrices A1, A2, and A3
Solution
A1 = [3
2
4]
A2 = [4
3
3]
A3 = [ 1
0
-1]
A = [ 3 4 1
2 3 0
4 3 -1]
B = [1
0
-2]
For b matrix to be consistent,
x1a1 + x2a2 + x3a3 = b
[3 4 1 1
2 3 0 0
4 3 -1 -2]
R2 -> R2 - 1/2R3
[ 3 4 1 1
0 3/2 1/2 1
4 3 -1 -2]
R3 -> R3 - 4/3R1
[3 4 1 1
0 3/2 1/2 1
0 -7/3 -7/3 -10/3]
Since, it means that system of equations corresponding to the vector equation x1a1 + x2a2 + x3a3 = b is consistent, so b is a linear combination of a1, a2, and a3 .
![Let matrices b,A1,A2,A3 be given by b=[1 0 -2] A1=[3 2 4] A2=[4 3 3] A3=[1 0 -1] Verify whether or not the matrix b is a linear combination of the matrices A1,](/WebImages/47/let-matrices-ba1a2a3-be-given-by-b1-0-2-a13-2-4-a24-3-3-a31-1147329-1761616990-0.webp "Let matrices b,A1,A2,A3 be given by b=[1 0 -2] A1=[3 2 4] A2=[4 3 3] A3=[1 0 -1] Verify whether or not the matrix b is a linear combination of the matrices A1,")
![Let matrices b,A1,A2,A3 be given by b=[1 0 -2] A1=[3 2 4] A2=[4 3 3] A3=[1 0 -1] Verify whether or not the matrix b is a linear combination of the matrices A1,](/WebImages/47/let-matrices-ba1a2a3-be-given-by-b1-0-2-a13-2-4-a24-3-3-a31-1147329-1761616990-1.webp "Let matrices b,A1,A2,A3 be given by b=[1 0 -2] A1=[3 2 4] A2=[4 3 3] A3=[1 0 -1] Verify whether or not the matrix b is a linear combination of the matrices A1,")
