Q10.
For a given matrix A = . Which of the following is true
(1) rank (A) = 3, nullity (A) = 1
(2) rank (A) = 2, nullity (A) = 2
(3) rank (A) = 1, nullity (A) = 3
(4) None of the given answers is true.
Q11.
For a, b R, the transformation T : R^2 R^3 defined byT (x, y) = (2x - y, 3x + y + 3A, 5x - 2y + bxy) is linear if
(1) a = b = 1
(2) a = 0; b = 1
(3) a = 1; b = 0
(4) None of the given answers is true.
Q12.
Suppose T : R^3 R^2
is a linear defined by
T (x, y) = (4x + 3y + Z, x - 2y). Then which of the following is basis of range T is
(1) (4, 1, 3), (1, 2, 0)
(2) (1, 0), (0, 1), (1, 1)
(3) (4, 1), (3, 2), (1, 0)
(4) None of the given answers is true.
Q 10
Reduced row Echolon form of A
Rank (A)= 1, Nullity (A) =3
Q 11
If T is linear it should satisfy
T(cx,cy)=cT(x,y)
For any scalar c, and any element x,y in the domain of T.
T(cx,cy)= (2cx-cy, 3cx+cy+3a, 5cx-2cy+bcxcy)
c(2x-y, 3x+y+3a, 5x-2y+bxy)
None of the given answer is true.
Q 12
Transforming matrix
rref A
Basis for range T is (1,0),(0,1)
None of the given answers is true.
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