Question 12, Exercise 2.1
Solutions of Question 12 of Exercise 2.1 of Unit 02: Matrices and Determinants. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.
Question 12(i)
Let A=[321456−234]. Verify thatA+At is symmetric.
Solution
A=[321456−234] At=[34−2253164] For symmetric, we have, (A+At)t=A+At A+At=[321456−234]+[34−2253164] =[3+32+41−24+25+56+3−2+13+64+4] A+At=[66−16109−198] (A+At)t=[66−16109−198] (A+At)t=(A+At)
Question 12(ii)
Let A=[321456−234]. Verify thatA−At is skew symmetric.
Solution
A=[321456−234] At=[34−2253164] For skew-symmetric, we have, (A−At)t=−(A−At) A−At=[321456−234]−[34−2253164] =[3−32−41+24−25−56−3−2−13−64−4] A−At=[0−23203−3−30] (A−At)t=[02−3−20−3330] (A−At)t=−[0−23203−3−30] (A−At)t=−(A−At)
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