2. define a linear transformation t: r^2 --> r^2 hras follows: t(x1, x2) = (x1 - 12,21 + x2). show that t is invertible and find t-1:

Step-by-step explanation:

Given:

Linear transformation,

  defined as

To Show: T is invertible

To find:

We know that Standard Basis of R² is

So, The matrix representation of T is

Now, Determinant of T = 1 - (-1) = 1 + 1 = 2 ≠ 0

⇒ Matrix Representation of T is Invertible matrix.

⇒ T is invertible Linear Transformation.

Hence Proved.

let,

Add (1) and (2),

Putting this value in (1),

Now,

Therefore,

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.