It's D yeah you're correct

0 votes

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

0

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

0

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 "

Magma Please enlighten this point

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

1

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

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