Let , ( ) be the values of m, for which the equations x + y + z = 1, x + 2y + 4z = m and x + 4y + 10z = m2 have infinitely many solutions. Then the value of n=110(n + n ) is equal to :
(4) 440
=0 always; infinitely many solutions ⇒ equations consistent
R2-R1: y+3z=m-1; R3-R1: 3y+9z=m2-1
R3-3R2: 0=m2-3m+2 ⇒ m=1,2
∴ n=110(n+n2)=55+385=440
Answer: (4)
If the system of equations 2x-y+z=4 5x+ y+3z=12 100x-47y+ z=212 has infinitely many solutions, then -2 is equal to
For some a,b, let f(x)= vmatrixa+ xx&1&b\ &1+ xx&b\ &1&b+ xx vmatrix, x 0, x 0f(x)= + a+ b. Then ( + + )2 is equal to :
If the system of equations x+2y-3z=2 2x+ y+5z=5 14x+3y+ z=33 has infinitely many solutions, then + is equal to :
If the system of equations ( -1)x+( -4)y+ z=5 x+( -1)y+( -4)z=7 ( +1)x+( +2)y-( +2)z=9 has infinitely many solutions, then 2+ is equal to
If A, B, and (adj (A-1 )+adj (B-1 ) ) are non-singular matrices of same order, then the inverse of A (adj (A-1 )+adj (B-1 ) )-1B, is equal to
The system of equations x+y+z=6, x+2y+5z=9, x+5y+ z= , has no solution if
Let A be a square matrix of order 3 such that (A)=-2 and (3 adj (-6 adj(3A) ) )=2m+n 3mn, m>n. Then 4m+2n is equal to .
If the system of linear equations : x+y+2z=6 2x+3y+az=a+1 -x-3y+bz=2b where a,b , has infinitely many solutions, then 7a+3b is equal to :
For a 3 3 matrix M, let trace (M) denote the sum of all the diagonal elements of M. Let A be a 3 3 matrix such that |A|= 12 and trace (A)=3. If B=adj(adj(2A)), then the value of |B|+ trace (B) equals :