Linear Alegbra MATRIX True and False Write TRUE if the state

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).

Solution

solution:

a) false

b) true

c)false

d) true

e)false

f) true

g) true

h)true