Write each of the following linear combinations of columns as a linear system of the form in (4): a) x_1begin{bmatrix}2 0 end{bmatrix}+x_2begin{bmatri

Amari Flowers 2021-03-11 Answered
Write each of the following linear combinations of columns as a linear system of the form in (4):
a)x1[20]+x2[13]=[42]
b)x1[121]+x2[012]+x3[345]+x4[134]=[258]
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Expert Answer

Yusuf Keller
Answered 2021-03-12 Author has 90 answers
Step 1
Given:
a)x1[20]+x2[13]=[42]
b)x1[121]+x2[012]+x3[345]+x4[134]=[258]
Step 2
a)x1[20]+x2[13]=[42]
Use the definition of scalar multiplication, we get
[2x10x1]+[1x23x2]=[42]
Using addition of matrix
[2x1+x20x1+3x2]=[42]
On comparing matrices, we get
2x1+x2=4
3x2=2
Step 3
b)x1[121]+x2[012]+x3[345]+x4[134]=[258]
Using the definition of scalar mutiplication, we get
[1x12x11x1]+[0x21x22x2]+[3x34x35x3]+[1x43x44x4]=[258]
Usinge addition of matrices, we get
[1x1+0x2+3x3+1x42x1+1x2+4x3+3x41x1+2x2+5x3+4x4]=[258]
On comparing matrices, we get
1x1+3x3+1x4=2
2x1+1x2+4x3+3x4=5
1x1+2x2+5x3+4x4=8
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Jeffrey Jordon
Answered 2022-01-27 Author has 2064 answers

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