Question

True or False

(5). Suppose the matrix A and B are both invertible, then (A + B)−1 = A−1 + B−1

. (6). The linear system ATAx = ATb is always consistent for any A ∈ Rm×n, b ∈Rm .

(7). For any matrix A ∈Rm×n , it satisfies dim(Nul(A)) = n−rank(A).

(8). The two linear systems Ax = 0 and ATAx = 0 have the same solution set.

(9). Suppose Q ∈Rn×n is an orthogonal matrix, then the row echelon form of Q has n leading variables.

(10). If matrix A ∈Rm×n, then rank(A) ≤ max{m,n}.

Answer 1