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The system of equations x + y + z = 6, 2x + y + z = 7, x + 2 y + z = has

a. A unique solution

b. No solution

c. An infinite number of solutions

d. None of these

in Linear Algebra by Boss (33k points)
edited by | 73 views
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Ax = b has a unique solution if and only if rank[A] = rank[A|b] = n where n is number of unknown variables 

3 Answers

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Answer Unique Solution
by (81 points)
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x + y + z = 6, 2x+ y +z = 7, x + 2 y +z = 8

              

1 1 1 6
2 1 1 7
1 2 1 8

we can also find it using Rank 

Ax = b has a unique solution if and only if rank[A] = rank[A|b] = n where n is number of unknown variables 

rank[A] = rank[A|b] = 3 

hence unique solution

by Active (4.2k points)
0 votes

Option a

by Boss (36.7k points)
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