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The lower triangular matrix [L] in the [L][U] decomposition of the matrix given below
is
Let be two matrices. Then the rank of P + Q is ______.
Let A and B two n × n matrices over real numbers. Let rank(M) and det(M) denote the rank and determinant of a matrix M, respectively. Consider the following statements.
I. rank(AB) = rank(A) rank(B)
II. det(AB) = det(A) det(B)
III. rank(A + B) ≤ rank(A) + rank(B)
IV. det(A + B) ≤ det(A) + det(B)
Which of the above statements are TRUE?
65 videos|120 docs|94 tests
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65 videos|120 docs|94 tests
|