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  3. (a) the n × n matrices a, b, c, and x satisfy the

(a) The n × n matrices A, B, C, and X satisfy the equation AX(B +...

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Basic Math

(a) The n × n matrices A, B, C, and X satisfy the equation AX(B+ CX) ?1 = C Write an expression for the matrix X in terms of A, B,and C. You may assume invertibility of any matrix whennecessary.

(b) Suppose D is a 3 × 5 matrix, E is a 5 × c matrix, and F is a4 × d matrix. Find the values of c and d for which the statement“det(DEF) = 1” can be valid. Explain your answer.

(c) Find all (real or complex) values of x such that the matrixGH is invertible, where G =

x^2, ?1

x , x ? 2

H = x ? 1 , ?2

1 , x + 1

Answer & Explanation Solved by verified expert
4.3 Ratings (778 Votes)
a Given AXBCX1 Cie AXBCX1BCX CBCXie AX CBCXie AX CBC2Xie AXC2X CBie AC2X CBie AC21AC2X AC21CBie X AC21CB Since inverses ofall matrices existsTherefore the required    See Answer
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