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Let {v_{1}, v_{2}, ........,v_{16}} be an ordered basis for V= C^{16}. If T is a linear transformation on V defined by T(v) = v_{i+1 }for 1 ≤ i ≤ 15 and T(v_{16}) = (v_{1} + v_{2} + ... + v_{16}) Then,
Let T : R^{3} > R^{3} be a linear transformation defined by T(x, y, z) =(x + y  z, x + y + z, y  z)
Then, the matrix of the linear transformation T with respect to the ordered basis B = {(0,1,0), (0,0,1), (1,0, 0) of R^{3} is
Let T : R^{4} > R^{4} be the linear map satisfying
T{e_{1}) =e_{2}, T(e_{2}) = e_{3}, T(e_{3}) = 0, T(e_{4}) = e_{3},
where {e_{1} e_{2}, e_{3} e_{4}} is the standard basis of R^{4}. Then,
Consider the basis {u_{1} u_{2}, u_{3}} of R^{3}, where u_{1} = (1, 0, 0), u_{2} = (1,1,0) , u_{3 }= (1,1,1) . Let {f_{1}, f_{2}, f_{3}} be the dual basis of {u_{1}, u_{2}, u_{3}} and f be a linear functional defined by f(a,b,c) = a + b + c, (a, b, c) ∈ R^{3}. If f = a_{1}f_{1} + a_{2}f_{2} + a_{3}f_{3} then (α_{1}, α_{2}, α_{3}) is
For a matrix [M] = , the transpose of the matrix is equal to the inverse of the matrix [M]' = M 1 The value of x is
If A is a nonzero column vector (n x 1), then the rank of matrix ,AA^{'} is
If P and Q are nonsingular matrices, then for matrix M, which of the following is correct?
If the rank of an n x n matrix A is (n  1), then the system of equations Ax= b has
Let A be a matrix of order m x n and R is nonsingular matrix of order n, then
Let A be a square matrix of order n, then nullity of A is
A is a 3 x 4 real matrix and AX = b is an inconsistent system of equations. The highest possible rank of A is
The system of linear equations 4x + 2y =7, 2x + y = 6 has
If x + 2y  2u = 0, 2x  y  u = 0, x + 2z  u = 0, 4x y + 3 z  u= 0 is a system of equations, then it is
Let T : P_{3}[0 ,1] > P_{2}[0 , 1] be defined by (T_{p}) (x) = P"(x) + P'(x). Then the matrix representation of T with respect to the basis {1, x, x^{2}, x^{3}} and {1, x, x^{2}} of P_{3}[0, 1] and P_{2}[0, 1], respectively is
Let T : R^{4 }—> R^{4} be defined by
T(x, y , z, w) = (x + y + 5w, x + 2 y + w,  y  z + 2w, 5x + y+ 2z).
Then dimension of the eigen space of T is
27 docs150 tests

27 docs150 tests
