Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1 According to that, an equivalent equation to the previous shown is. O a) X = (C-1+1515)A¯'(B")-1 Ob) X = A-(C-1 + 151;)(B")-1 Oc) X = (B")-'(C-+1515)A¬! O d) X = A-(B")"(C-1+15I5)

etA = Compute the matrix exponential e for the matrix A 6e^(-2t)-5€ -3e^(-2t)+3 10e^(-2t)-1 -25e^(-2t)+ -17 9 -30 16 Note the t!

The matrix A = (13¹) is closely related to the imaginary number i. (a) Calculate A², A³, A4, expressing each as a multiple of either A or the identity matrix I. Infer the general pattern for A4, A4n+1, A4n+2 A4n+3, where n is an integer, and notice how this compares to powers of i (b) The exponential of a matrix is defined in terms of the power series eX = 1 + X + ² X ²X² + ²/1 ² Calculate e, evaluating the series to obtain a simple 2 x 2 matrix. Explain the result geometrically, noting the close analogy with e ·X³+.

Express the quadratic equation in the matrix form x Ax + Kx + f = 0, where x Ax is the associated quadratic form and K is an appropriate matrix. ¹-(- -) A = K = y² + 2x - 3y1 = 0, |ƒ =

[EX4 Q2] A matrix question :)

Solve the matrix equation AX = B for X. 12 ^-]-[] B = 6 7 A = X || 18 14 59