write B as a linear combination of the other matrices, if possible. B=begin{bmatrix}2 & 3 -4 & 2 end{bmatrix} , A_1=begin{bmatrix}1 & 0 0 & 1 end{bmatrix} , A_2=begin{bmatrix}0 &-1 1 & 0 end{bmatrix} , A_3=begin{bmatrix}1 &1 0 & 1 end{bmatrix}

waigaK 2020-11-07 Answered
write B as a linear combination of the other matrices, if possible.
B=[2342],A1=[1001],A2=[0110],A3=[1101]
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Arnold Odonnell
Answered 2020-11-08 Author has 109 answers
Given
The given matrix is
B=[2342],A1=[1001],A2=[0110],A3=[1101]
Calculation:
Let us represent B as a linear combination of A1,A2,A3
B=c1A1+c2A2+c3A3
[2342]=c1[1001]+c2[0110]+c3[1101]
=[c100c1]+[0c2c20]+[c3c30c3]
=[c1+0+c30c2+c30+c2+0c1+0+c3]
Step 3
Now , by comparing both sides.
c1+0+c3=2(1)
0c2+c3=3(2)
0+c2+0=4(3)
c1+0+c3=2(4)
from equation (3) and (2)
c2=4 and c3=1
substitute c3=1 in (1) we get c1=3
Thus ,we can say B=3A14A2A3
Not exactly what you’re looking for?
Ask My Question
Jeffrey Jordon
Answered 2022-01-27 Author has 2064 answers

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more