Write the homogeneous system of linear equations in the form AX = 0. Then verify by matrix multiplication that the given matrix X is a solution of the

smileycellist2 2021-03-04 Answered
Write the homogeneous system of linear equations in the form AX = 0. Then verify by matrix multiplication that the given matrix X is a solution of the system for any real number c1
{x1+x2+x3+x4=0x1+x2x3+x4=0x1+x2x3x4=03x1+x2+x3x4=0
X=(1111)
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d2saint0
Answered 2021-03-05 Author has 89 answers

Lets write
A=[1111111111113111]X=[x1x2x3x4]
Matrix A , which has the dimensions 4×4, is the matrix of ciefficients of the system , X , which has the dimensions 4×1 is the matrix of unknowns.
AX=0
[1111111111113111][x1x2x3x4]=[0000]
If X is a solution of SX=0 , then so is c1 for any constant c1 . compute the product AX:
AX=[1111111111113111][1111]
=[11+1(1)+1(1)+1111+1(1)+(1)(1)+1111+1(1)+(1)(1)+(1)131+1(1)+1(1)+(1)1]=[0000]

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