Prove that the following. `[[a+d,a+d+k,a+d+c],[c,c+b,c],[d,d+k,d+c]]`=abc

Prove that the following sets A,B,C D are equivalent. Where A={1,2,3,4,...},B={2,4,6,8,...},C={1,3,5,7,} D={1,8,27,64,125,...}.

Prove that the lines x = ay + b, z = cy + d and x = a'y + b' , z= c'y + d' are perpendicular, if a a' + c c' + 1=0

Find the following products . [{:(0,k),(1,0):}][{:(a,b),(c,d):}]

Match the animals given in column A with their location in column B. {:(,"Column A",,"Column B"),((i),"Dodo",A.,"Africa"),((ii),"Quagga",B.,"Russia"),((iii),"Thylacine",C.,"Mauritius"),((iv),"Stellar's sea cow",D.,"Australia"):} Choose the correct match from the following. (a) i-A, ii-C, iii-B, iv-D (b) i-D, ii-C, iii-A, iv-B (c) i-C, ii-A, iii-B, iv-D (d) i-C, ii-A, iii-D, iv-B

Find the following products . [{:(1,0),(0,k):}][{:(a,b),(c,d):}]

Find the following products . [{:(0,1),(1,0):}][{:(a,b),(c,d):}]

Find the following products . [{:(a,b),(c,d):}][{:(0,1),(1,0):}]

Photosynthetic pigments of Rhodophyceae (red algae) are a. chl a and b b. chl a and c, fucoxanthin c. chl a and d d. chl a,chl d and phycoerythrin.

Show that the relation S defined on set N xx N by (a, b) S(c,d) rArr a+d=b+c is an equivalence relation.

Find the value of a if [[a-b,2a+c],[2a-b,3c+d]]=[[-1,5],[0,13]] .