Define N epsilon LF5 by NXl X2 X3 X4 X5 2x2 3x3 x4 4x5 0Fi

Define N epsilon L(F^5) by N(X_l, X_2, X_3, X_4, X_5) = (2x_2, 3x_3, - x_4, 4x_5, 0).Find a squareroot of I + N

Solution

N is a linear transformation from F⁵ to F⁵ (trivial)

the matrix representing N can be found out by finding where the basis elements are transformed to.

N+I will be matrix. If we can find an A such that A² = N+I.

Then, A is the required result.