Linear Alegbra( MATRIX) True and False Write \"TRUE\" if the statement Is true a

Question

Linear Alegbra( MATRIX)

True and False

Write "TRUE" if the statement Is true and " FALSE" if the statement is false hi the space provided. Each correct answer worth 3 points. For matrices A and B, (AB)_T = A_TB_T. For matrices A and B, (AB)^-1 = b^-1 A^-1. If A and B are invertible n times n matrices then A+B is invertible and (A + B)^-1 = A^-1 + B^-1 If A is a square matrix with two columns of A equal, then det(A) = 0. If B is a square matrix of order 3 with det(B) = -1, then det(2B^3) = -8. If det(A) = 0, then the homogeneous system AX = 0 has infinitely many solutions. If det(A) = 0, then the system AX = b has infinitely many solutions. If A is an n times n matrix with det(A) = 1, then A^-1 = adj(A).

Explanation / Answer

solution:

a) false

b) true

c)false

d) true

e)false

f) true

g) true

h)true

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