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Question: Maple Matrix Question

Question:Maple Matrix Question

HBKodak 55 Maple
linear-algebra homework
May 02 2022
1

Let 
                              "a"

 and 
                              "b"

 be real numbers and 

       
"A = Matrix(3, 3, [[a, a - 1, -b], [a - 1, a, -b], [b, b, 2*a - 

   1]])"


,  
                              "B="


 "Matrix(5, 5, [[0, a, 3, 0, a], [3, 0, 0, b, 0], [0, 1, b, 0, 

    1], [b, 0, 0, 1, 0], [0, a, 1, 0, b]])"


. 

(a) Show that if 
                            "0 <= a"

, 
                            "a <= 1"

 and 
                      "b^2 = 2*a*(1 - a)"

, then A is an orthogonal matrix with determinant equal to one. 
(b) For what values of a and b is the matrix B singular? Determine the inverse of B (for those values of a and b for which B is invertible).
 
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