For each of the following statements decide whether it is true (T) or false (F).
ID: 2900129 • Letter: F
Question
For each of the following statements decide whether it is true (T) or false (F). Substantiate your decision (a reminder: in case you wish to prove that the statement is false, a single counterexample provides a sufficient argument). For two n times n matrices A and B, del (A + B) = det A + det B. The cofactor of a diagonal entry of a square matrix is equal to the minor associated with that entry. det(-/f) = -detA A determinant does not change as a result of the following two operations: one of its columns is multiplied by 1/3, and one of its rows is multiplied by 3. det(A) = (det A)". If A and P are square matrices of the same size, and P is invertible, det (PAP^-1) = det A. A square matrix is invertible if the RREF of this matrix is invertible. A system of linear equations is Cramer's iff it has a unique solution.Explanation / Answer
(a)false
(b)true because (-1)^(i+j) is always 1 for diagonal elements
(c)false it depends on the value of n,if n is even
(d)true
(e)true
(f)true
(g)true
(h)true
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