(A) Given transformation is :
Let A = (x,y) and B = (u,v) .
Then, and
Now,
And,
Then,
Therefore, the given transformation is not linear.
(B) Given transformation is :
Let A = (x,y) and B = (u,v) .
Then, and
Now,
i.e.,
Therefore, the given transformation is not linear.
(D) Given transformation is :
Let A = (x,y) and B = (u,v) .
Then, and
Now,
i.e.,
i.e.,
i.e.,
Therefore, the given transformation is linear.
(E) Given transformation is :
Let A = (x,y) and B = (u,v) .
Then, and
Now,
i.e.,
Therefore, the given transformation is not linear.
Which of the following transformations T R2 → R is linear? A. T(x,y)=5 OB. T(x,y) =...
Determine whether the following transformations are linear. A) T(x, y) = (3x, y, y ? x) of R2 ? R3 B) T(x, y) = (x + y, 2y + 5) of R2 ? R2
Which of the following are linear transformations? f: R3 R2 [x, y, z] [7x - 2y, 0 h R R x > sin x g R2R [x, y] [y- x, 2 the map T R > R< described by reflection in a line L: 2x + 7y = 0 through the origin.
2. Consider the following transformations of R2 Tİ (z, y) (-r, y), T3(x, y) (z, _y), T,(zw) (y, x). Show that, for any j 1,2,3, a subset A C R2 is a Jordan region if and only if T,(A) is a Jordan region. What is the relation between the volumes of A and T, (A)? 2. Consider the following transformations of R2 Tİ (z, y) (-r, y), T3(x, y) (z, _y), T,(zw) (y, x). Show that, for any j 1,2,3,...
5. Solve the initial-value problem associated with the linear first-order ODE z y + * In(x) y = 2e3x y(1) = 0, O O where the prime stands for differentiation with respect to x. O A. y = r-> (3x + Ke"), where K is an arbitrary constant. B.y=r" (e3+ Ke*), where K is an arbitrary constant. C.y=r-(+2 – 23). OD. y = x* (032 – *+2). O E. y = x-P(.38 – 42+2). OE y = x? (032 –...
Write the equation with rectangular coordinates. r2 = 5 cos20 a. (x2 + y2)2 = 5(x2 + y2) ob. (x2 + y2)2 = 6(x2 –y?) Oc. (x² + y2)2 = 6(x2+y?) O d. (x+y?)? = 6(x2-y?) O e. (x2+x2)? = 5(x2-y2)
1. Consider the unit circle: (x,y) : x2 y2 = 1. T. Let f R2 ->R be defined by f(x,y) = x2-y, and let F : R2 -> R be defined by F(x, y) Compute the integral of f and F around the unit circle. For the integral of F, proceed in the standard (anticlockwise) direction
Which of the following transformations are linear? > 5 || S 5 832 321 > 1 S 5 || || | || a007 | || S S S S S S = = = = = 7x1 + x2 --21 2x1 -- 5x2 + 6x3 9x2 – 7x3 -431 – 822 21 +9 22 S 5 y 1 y2
determine weather the following mappings are linear transformations. Either prove that the mapping is a linear transformation to explain why it is not a linear transformation. a)T:R3[x] to R3[x] given by T(p(x))=xp'(x)+1, where f'(x) is a derivative of the polynomial p(x). b) T:R2 to R2 given by T([x y])=[x -y]. Additionally describe this mapping in part b geometrically.
(1 point a. The linear transformation T : R2 → R2 is given by: Ti (x, y) = (2x + 9y, 4x + 19y). Find T1x, y). 「-i(x, y) =( x+ y, x+ b. The linear transformation T2 : R' → R' is given by: T2(x, y, z) (x + 2z,2r +y, 2y +z) Find (x, y, z). T2-1(x,y,z)=( x+ y+ z, x+ y+ z, x+ y+ z)
linear algebra Find the matrix A' for T relative to the basis B'. T: R2 R2, T(x, y) = (-3x + y, 3x - y), B' = {(1, -1), (-1,5)} A' =