Im doing a self review,, i ran out of questions for my subscription, please only
ID: 3185626 • Letter: I
Question
Im doing a self review,, i ran out of questions for my subscription, please only attempt if u are doing most of them.. as u can see i have some question written ,,please try to answer them...thank u..Any helpful help would be much appreciated, guaranteed... i falsc phase Ue or false VC (e) If A is a 4 x 3 matrix, then rank(A) can be at most 4 (d) A systern of linear equations written in the form Az = b has a solution iff rank(A) = rank(A) al (e) f A and B have the same sizes and rank(4) - rank(B) then rank(A + B) - rank(A) - RanklB) e (f)1f A is n × n and IA|-10then IcA|-c10 (g) lAis n × n and Ais a singularmatrix then rank(A) Sn-1 cis a constant" - alse fals e h) (AB)-1 -B- b) Falr why
Explanation / Answer
( c). False. The row rank and the column rank are equal. Henk the rank(A) can be at most 3.
(d). True. If the ranks of the coefficient and the augmented matrices are equal, then there is always a solution to AX = b.
(e). False. If A = I2 and B = -I2, then rank(A) = rank(B) = 2, while rank(A+B) = 0 as A+B is a 2x2 zero matrix.
(f). True. The norm, of a mxn matrix A is defined as the square root of the sum of the absolute squares of its elements. Also, in the scalar multiple of a matrix, all the elements of the matrix get multiplied by the scalar.
(g).True. The rank of a matrix is the maximum number of independent rows. If a matrix is singular, all its rows are not linearly independent.
(h). False. (AB)-1 = B-1 A-1. Also, (B-1 A-1)T = (A-1)T (B-1)T. Hence, ((AB)-1)T = (B-1 A-1)T =(A-1)T (B-1)T.