Example 1:
Find the product of the following pairs of matrices.
(a) (1 5 2)(243)(b) (28−31)(104−2)(c) (−35)(2 6)(d) (04−13)(7−2)(e) (7 −4)(−20−13)
Solution:
(a) (1 5 2)(243)←Matrices analysis1×3 and 3×1 ↓ ↓=1×1 matrix=(1×2 ⊕ 5×4 ⊕ 2×3)=(2+20+6)=(28)
(b)
(28−31)(104−2)←Matrices analysis2×2 and 2×2 ↓ ↓=2×2 matrix=(2×1+8×4 2×0+8×−2−3×1+1×4 −3×0+1×−2)=(34−161−2)
(c)
(−35)(2 6)←Matrices analysis2×1 and 1×2 ↓ ↓=2×2 matrix=(−3×2 −3×65×2 5×6)=(−6−181030)
(d)
(04−13)(7−2)←Matrices analysis2×2 and 2×1 ↓ ↓=2×1 matrix=(0×7+4×−2−1×7+3×−2)=(−8−13)
(e)
(7 −4)(−20−13)←Matrices analysis1×2 and 2×2 ↓ ↓=1×2 matrix=(7×−2+(−4×−1) 7×0+(−4×3))=(−14+4 0−12)=(−10 −12)
Find the product of the following pairs of matrices.
(a) (1 5 2)(243)(b) (28−31)(104−2)(c) (−35)(2 6)(d) (04−13)(7−2)(e) (7 −4)(−20−13)
Solution:
(a) (1 5 2)(243)←Matrices analysis1×3 and 3×1 ↓ ↓=1×1 matrix=(1×2 ⊕ 5×4 ⊕ 2×3)=(2+20+6)=(28)
(b)
(28−31)(104−2)←Matrices analysis2×2 and 2×2 ↓ ↓=2×2 matrix=(2×1+8×4 2×0+8×−2−3×1+1×4 −3×0+1×−2)=(34−161−2)
(c)
(−35)(2 6)←Matrices analysis2×1 and 1×2 ↓ ↓=2×2 matrix=(−3×2 −3×65×2 5×6)=(−6−181030)
(d)
(04−13)(7−2)←Matrices analysis2×2 and 2×1 ↓ ↓=2×1 matrix=(0×7+4×−2−1×7+3×−2)=(−8−13)
(e)
(7 −4)(−20−13)←Matrices analysis1×2 and 2×2 ↓ ↓=1×2 matrix=(7×−2+(−4×−1) 7×0+(−4×3))=(−14+4 0−12)=(−10 −12)