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✷✳ ▼❆❚❘■❩❊❙ ✷✺ ✷✳✶✯ ❙❡❥❛♠ A= [ 1 −2 3 4 1 0 ] ❡ B= [ −1 2 0 1 −2 0 ] ✳ ❈❛❧❝✉❧❡ 2A✱ 3B ❡ 2A−3B✳ ✷✳✷ ❉❡.❡/♠✐♥❡ ♦3 ✈❛❧♦/❡3 ❞❡ x, y ❡ z ❡♠ R ♣❛/❛ 7✉❡ ❛3 ♠❛./✐③❡3 A ❡ B ❞❛❞❛3 3❡❥❛♠ ✐❣✉❛✐3✿ A = [ x+ y 0 z x− 2y ] ❡ B = [ 13 0 1 4 ] ✳ ✷✳✸ ❉❛❞❛3 ❛3 ♠❛./✐③❡3 A = [ −1 4 −2 2 0 −1 ] , B = [ 0 1 −2 0 1 −1 ] , C = 1 1 3 ❡ D = [−1 1], ❞❡.❡/♠✐♥❡✿ ✭❛✮ A+B❀ ✭❜✮ −2C❀ ✭❝✮ AC❀ ✭❞✮ CD❀ ✭❡✮ BC❀ ✭❢✮ DA✳ ✷✳✹✯ ❈♦♥3✐❞❡/❡ ❛3 ♠❛./✐③❡3 A = [aij]4×5 ❝♦♠ aij = i− j, B = [bij]5×9 ❝♦♠ bij = j ❡ C = [cij] ❝♦♠ C = AB. ✭❛✮ ➱ ♣♦33A✈❡❧ ❞❡.❡/♠✐♥❛/ c63❄ ❏✉3.✐✜7✉❡ ❛ /❡3♣♦3.❛✳ ✭❜✮ ❉❡.❡/♠✐♥❡ c36✳ ✷✳✺ ❈♦♥❝❧✉❛ ❛3 ❞❡♠♦♥3./❛EF❡3 ❞❛3 G/♦♣♦3✐EF❡3 ✶✳✷✳✶✱ ✶✳✷✳✷ ❡ ✶✳✷✳✸✳ ✷✳✻✯ ❉❛❞❛ ✉♠❛ ♠❛./✐③ A✱ ❞✐③❡♠♦3 7✉❡ ✉♠❛ ♠❛./✐③ X ❝♦♠✉$❛ ❝♦♠ A 3❡ AX = XA✳ ❉❡.❡/♠✐♥❡ .♦❞❛3 ❛3 ♠❛./✐③❡3 7✉❡ ❝♦♠✉.❛♠ ❝♦♠ A = [ 1 0 0 3 ] . ✷✳✼ ❛✮ ▼♦3./❡ 7✉❡ ❛ ♠❛./✐③ c In✱ ♦♥❞❡ c ∈ R✱ ❝♦♠✉.❛ ❝♦♠ .♦❞❛ ♠❛./✐③ X ∈ M(n, n)✳
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