write B as a linear combination of the other matrices, if possible. B=begin{bmatrix}2 & 5 0 & 3 end{bmatrix} , A_1=begin{bmatrix}1 & 2 -1 & 1 end{bmatrix} , A_2=begin{bmatrix}0 &1 2 & 1 end{bmatrix}

necessaryh 2021-01-15 Answered
write B as a linear combination of the other matrices, if possible.
B=[2503],A1=[1211],A2=[0121]
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Expert Answer

hajavaF
Answered 2021-01-16 Author has 90 answers
Step 1
Given B=[2503],A1=[1211],A2=[0121]
Here we write B is a linear combination of the other matrices .
Step 2
Let us consider the relation
B=C1A1+C2A2(A) where C1,C2 are arbitary constant
[2503]=C1[1211]+C2[0121]
[2503]=[C1+0C22C1+C2C1+2C2C1+C2]
C1=2,(1)2C1+C2=5,(2)C1+2C2=0(3)
 and C1+C2=3(4)
 put C1=2 we get
2x2+C2=5
C2=54=1
Also C1=2 and C2=1 satisfy the equation (3) and (4)
Step 3
Hence From (A)
B=2A1+A2
B=2[1211]+[0121]
Hence B is a linear combination of A1 and A2 .
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Jeffrey Jordon
Answered 2022-01-24 Author has 2047 answers

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