Ex 3.2, 3

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Ex 3.2, 3 Compute the indicated products (i)[■8(a&b@−b&a)] [■8(a&−b@b&a)] [■8(a&b@−b&a)]_"2 × 2" [■8(a&−b@b&a)]_"2 × 2" = [■8( a×a+b×b&a× (−b)+b×a@−b×a+b×b&(−b)×(−b)+a×a)]_(2 × 2) = [■8(a2+b2&−ab+ab@−ab+ab&b2+a2)] = [■8(a2+b2&0@0&b2+a2)] Ex 3.2, 3 Compute the indicated products (ii)[█(1@2@3)][2 3 4] [█(1@2@3)]_(3 × 1)[2 3 4]1 × 3 = 〖" " [■8(1×2&1×3&1×4@2×2&2×3&2×4@3×2&3×3&3×4)]〗_(3 × 3) = [■8(2&3&4@4&6&8@6&9&12)] Ex 3.2, 3 Compute the indicated products (iii) [■8(1&−2@2&3)] [■8(1&2&3@2&3&1)] [■8(1&−2@2&3)]_"2 × 2" [■8(1&2&3@2&3&1)]_"2 × 3" = [■8(1×1+(−2)×2&1×2+(−2)×3&1×3+(−2)×1@2×1+3×2&2×2+3×3&2×3+3×1)]_(2 × 3) = [■8(1−4&2−6&3−2@2+6&4+9&6+3)] = [■8(−3&−4&1@8&13&9)] Ex 3.2, 3 Compute the indicated products (iv) [■8(2&3&4@█(3@4)&█(4@5)&█(5@6))] [■8(1&−3&5@█(0@3)&█(2@0)&█(4@5))] [■8(2&3&4@█(3@4)&█(4@5)&█(5@6))]_(3 × 3) [■8(1&−3&5@█(0@3)&█(2@0)&█(4@5))]_(3 × 3) = [■8(2×1+3×0+4×3&2×(−3)+3×2+4×0&2×5+3×4+4×5@3×1+4×0+5×3&3×(−3)+4×2+5×0&2×5+4×4+5×5@4×1+5×0+6×3&4×(−3)+5×2+6×0&2×5+5×4+6×5)]_(3 × 3) = [■8(2+0+12&−6+6+0&10+12+20@3+0+15&−9+0+0&15+16+25@4+0+18&−12+10+0&20+20+30)] = [■8(14&0&42@18&−1&56@22&−2&70)] Ex 3.2, 3 Compute the indicated products (v) [■8( 2&1@ 3&2@−1&1)] [■8( 1&0&1@−1&2&1)] [■8( 2&1@ 3&2@−1&1)]_(3 ×2) [■8( 1&0&1@−1&2&1)]_(2 ×3) = [■8(2×1+1×(−1)&2×0+1×2&2×1+1×1@3×1+2×(−1)&3×0+2×2&3×1+2×1@−1×1+(1)×(−1)&−1×0+1×2&−1×1+1×1)]_(3 × 3) = [■8(2−1& 0+2&2+1@3−2&0+4&3+2@−1−1&0+2&−1+1)] = [■8(1&2&3@1&4&5@−2&2&0)] Ex 3.2, 3 Compute the indicated products (vi) [■8(3&−1&3@−1&0&2)][■8(2&−3@1&0@3&1)] [■8(3&−1&3@−1&0&2)]_"2 × 3" [■8(2&−3@1&0@3&1)]_"3 × 2" = [■8(3(2)−1(1)+3(3)&3(−3)−1(0)+3(1)@−1(2)+0(1)+2(3)&−1(−3)+0(0)+2(1))]_(2 ×2) = [■8(6−1+9&−9−0+3@−2+0+6&3+0+2)] = [■8(14&−6@4&5)]