Answer to Question #94720 in Abstract Algebra for Daniel

Question

1. \\((p\\wedge q)= (q\\wedge p)\\) and \\((p\\vee q) = (q\\vee p)\\) implies an _____ a. Idempotent Laws b. Associative laws c. Distributive Laws d. Commutative Laws 2. given that\\(A=\\begin{pmatrix}1 & 2 & 3\\\\ 4 & 5 & 6 \\end{pmatrix}\\)\nand \\[B=\\begin{pmatrix} 1 & 2\\\\ 3& 4\\\\ 5& 6 \\end{pmatrix}\\]\n. Find AB a. \\(\\begin{pmatrix} 0 & 12 & 17\\\\ 19 & 26 & 31\\\\ 29 & 40 & 51 \\end{pmatrix}\\) b. \\(\\begin{pmatrix} 5 & 12 & 15\\\\ 19 & 26 & 31\\\\ 29 & 40 & 51 \\end{pmatrix}\\) c. \\(\\begin{pmatrix} 0 & 12 & 17\\\\ 19 & 26 & 31\\\\ 20 & 40 & 45 \\end{pmatrix}\\) d. \\(\\begin{pmatrix} 0 & 12 & 17\\\\ 7 & 10 & 31\\\\ 20 & 40 & 45 \\end{pmatrix}\\)

Answer 1

Q1 d) Commutative laws

Q2 Non of them is correct because

$A= \begin{pmatrix}1 & 2 & 3\\ 4 & 5 & 6 \end{pmatrix}$

$B= \begin{pmatrix} 1 & 2\\ 3& 4\\ 5& 6 \end{pmatrix}$

$AB =\begin{pmatrix}1*1+2*3+3*5 & 1*2+2*4+3*6 \\ 4*1+5*3+6*5 & 4*2+5*4+6*6 \end{pmatrix}= \begin{pmatrix}22 & 28 \\ 49 & 64 \end{pmatrix}$