System of Equations

Question

My solution:-

Since the Determinant of matrix is Zero. So it will posses non trivial solution. Now what should be the answer ?

According to me Option D as rank is  < Order so infinite number of solutions 

Comments

It's D  yeah you're correct

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Na462   what's the answer given ??

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Option D is correct.

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Answer given is B, maybe it's wrong.

What is condition for no solution In homogenous equations ?

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if in question they mentioned that Number of linearly independent solution

then it's equal to 1

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no solution In homogenous equations

In homogeneous linear equation 

always there's a unique solution which is x = y = z = 0

when rank (A)  = Number of variable

 

No solution is the case of Non homogenous equations

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Oh yeah I'm stupid socha nhi mene axche se thnks.

Magma Please enlighten this point

" if in question they mentioned that Number of linearly independent solution then it's 1  "

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if No of variables  = 3

and rank of matrix (A) = 2

No of linear independent solution : 3-2 = 1

which means if a equation is like that

x + 3y + 2z = 0

-7y + 8z = 0

therefore Y = (8/7) Z , X = (10/7) Z

let Z  = c

Y = (8/7)c , X = (10/7)C

for any arbitrary value of C we can get X and Y

therefore no of independent solution  = 1 from which we can derive infinite solution

 

Similarly if

if No of variables  = 3

and rank of matrix (A) = 1

No of linear independent solution : 3-2 = 1