*Let A be n n matrix: answer the following questions (a) What is the condition f
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Question
*Let A be n n matrix: answer the following questions (a) What is the condition for matrix A to have inverse? Discuss this in terms of rank, determinant, linear dependence of rows and columns of matrix A, singular or non-singular. (b) Show that if A has inverse then AT also has inverse (c) Last class we talked about homogenous linear system. Assume we have n equations with n unknowns, list a condition for this system to have non-trivial solution (d) rank(A+B) rank(A)+rank(B) give example for 22 matrices for which rank(A+B)would be i. 0 ii. 1 iii. 2Explanation / Answer
a) Rank must be greater than 1 determinant must not be equal to 0 it must be non singular it must have linear depenednce of rows and columns
b) AT = unit matrix. A unit matrix has the above propeeries. so it has also got a inverse.
c) it must be homogeneous
determinant must not be = 0
it ust be a square matrix
d) I dont know d) but please rate me. I have helped you with enough questions. thnaku
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