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The unique linear transformation such that T(1,2) = (2,3) and T(0,1) = (1,4). Then H rule for T is
Let V and W be vector spaces over be a map. Then T is a linear transformation iff
is a linear transformation T(1,0) = (2,3,l) and T(1,1) = (3,0,2) then which one of the following statement is correct?
Let T:R^{2} > R^{2} be the transformation T(x_{1},x_{2}) = (x_{1},0). The null space (or kernel) N(T) of T is
be the vector space of all complex numbers over complex field be defined by T(z) =
A^{A1 }= I =
Therefore, a = 1 / 60 and b = 1 / 3 and a + b = 7 / 20.
Let T: R^{3} → R^{3} be a linear transformation and I be the identify transformation of R3. If there is a scalar C and a nonzero vector x ∈ R^{3} such that T(x) = Cx, then rank (T – CI)
By ranknullity is theorem,
dim(T) = Rank(T) + Nullity (T)
Here dim(T) = 3 Now, (T – CI)x = T(x) – (T(x) = cx – cx
= 0
(I is identity transformation)
⇒ Nullity of T – CI cannot be zero
⇒ Hence, Rank of T – CI cannot be 3.
Which of the following Linear Transformations is not correct for the given matrix?
In the given question,
Thus, x_{1} = 1y_{1}  2y_{2}  3y_{3}
x_{2} = 1y_{1} + 1y_{3}
x_{3 }= 2y_{1} + y_{2}.
Applying inverse Fourier transform, we get
x(t) = e^{2t} u(t) + 5e^{4t} u(t).
Consider the basis S = {v_{1}, v_{2}, v_{3}} for where v_{1} = (1,1,1) and v_{2} = (1,1,0), v_{3} = (1,0,0) and let be a linear transformation such that T(v_{1}) = (1,0), T (v_{2}) = (2, 1), T (v_{3}) = (4, 3). Then T (2,  3, 5) is
Which one of the following is not a criterion for linearity of an equation?
The two criterions for linearity of an equation are: The dependent variable y and its derivatives of first degree. Each coefficient depends only on the independent variable.
Consider the following such that T(2,2) = (8,  6), T (5, 5) = (3,  2) Then
Let T be linear transformation on into itself such that T(1,0) = (1,2) and T (1, 1) = (0, 2) .Then T(a, b) is equal to
If is given by T (x, y, z) = (x  y, y + 3z, x + 2y). Then T^{1} is
According to the property of the Eigen values, the sum of the Eigen values of a matrix is its trace that is the sum of the elements of the principal diagonal.
Therefore, the sum of the Eigen values = 3 + 4 + 1 = 8.
Let T: R^{3} → R^{3}^{ }be a linear transformation and I be the identity transformation of R^{3}. If there is a scalar C and a nonzero vector x ∈ R^{3} such that T(x) = Cx, then rank (T – CI)
By ranknullity is theorem,
dim(T) = Rank(T) + Nullity (T)
Here dim(T) = 3
Now, (T – CI)x = T(x) – (T(x) = cx – cx = 0 (I is identity transformation)
⇒ Nullity of T – CI cannot be zero
⇒ Hence, Rank of T – CI cannot be 3.
where T be the reflection of the points through the line y = x then the matrix of T with respect to standard basis is
Consider the two linear mapsT_{1} and T_{2} on V_{3} defined as T_{1}(x_{1}, x_{2}, x_{3}) = (0, x_{2}, x_{3}) and T_{2}(x_{1}, x_{2}, x_{3}) = (x_{1}, 0,0)
Let T be a linear transformation on the vector space defined by T(a, b) = (a, 0) the matrix of T relative to the ordered basis {(1,0), (0,1)} of is
Let W be the vector space of all real polynomials of degree atmost 3. Define T : W → W by T(p(x)) = p'(x) where p'(x) is the derivative of P.The matrix of T in the basis {1, x, x^{2}, x^{3}} considered as column vector is given by
Let be the polynomial space with basis {1, x, x^{2}} then matrix representation of
Find the fourier transform of F(x) = 1, x < a0, otherwise.
Let be defined by T(p(x)) = p"(x) + p'(x). Then the matrix representation of T with respect to basis {1, x, x^{2}, x^{3}} and {1, x, x^{2}} of and respectively is
For the standard basis {(1,0,0), (0,1,0), (0,0,1)} of is a linear transformation T from has the matrix representation Then the image of (2,1,2) under T is
Let us consider a 3×3 matrix A with Eigen values of λ_{1}, λ_{2}, λ_{3 }and the Eigen values of A^{1 }are?
According to the property of the Eigen values, if is the Eigen value of A, then 1 / λ is the Eigen value of A^{1}. So the Eigen values of A^{1 }are 1 / λ_{1}, 1 / λ_{2}, 1 / λ_{3}.
Let be the map given by If the matrix of T relative to the standard basis β = γ = {1, x, x^{2}, x^{3}} is
A linear transformation T rotates each vector in clockwise through 90°. The matrix T relative to standard ordered basis
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