Let e,= The image of and e₂= , and y₂² 7 and let T: R² R2 be a linear transformation that maps e, into y, and maps e into y₂. Find the images of 5 and

Each of J, K, L, M and N is a linear transformation from R2 to R². These functions are given as follows: Jx1, х2) %3D (Зхі — 5х2, —6х1 + 10x), K(x1, x2) = (-V3x2, 3x1), L(x1, x2) = (x2, –x1), M(x1, x2) = (Зх1 + 5х, бх1 — бх2), N(x1, x2) = (-v5x1, v5x2). (a) In each case, compute the determinant of the transformation. . det J= ,det K ,det L= ,det M= ,det N

Show that the transformation Y = 2x, + xg + X3 Y2 = Xz + Xg + 2x ys = x,- 2rg is regular. Write down the inverse transformation.

Let -9 and 72 = -12] and let T: R² R2 be a linear transformation that maps ₁ to ₁ and maps e2 to 2. a. Find the image of T([3]) e₁ = T([22]) = b. Find the image of H [1] = 7₁ =

all of part (a) please

Name the type of transformation

I really need help with this asap please

Determine whether the function is a linear transformation. T: P₂ → P₂, Tao + a₁x + a₂x²) linear transformation O not a linear transformation = (ao + a₁ + a₂) + (a₁ + a₂)x + a2x²

Find Linear Fractional Transformation that maps the given three points onto the three given points in the respective order: Pr. 6. 0,1,2 onto 1,,; Pr. 7. 0,-i, i onto -1,0, o%3; Pr. 8. 0, 2i,-2i onto -1,0, oo.

Suppose a linear transformation: T:R2-->R2 is formed by taking a rotation counterclockwise of 180 degrees, followed by a reflection across the x2-axis. Describe the points that will be moved back to their original position by this transformation.