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Openai/695dfc16-b2ac-8005-980b-b86d96450929
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=== User: 12.將座標r114,514寫成矩陣R(114在上514在下),以下關於方陣的說法何者正確 === 12.將座標r(114,514)寫成矩陣R(114在上514在下),以下關於方陣的說法何者正確 (1)ABCR代表ABC三個方陣皆作用於R上,且作用順序為C→B→A (2)承上,如果C=A^-1,則對於任意方陣B,ABCR=BR皆成立,因為AA^-1=I2(二階單位方陣) (3)如果A是=上(2,3)下(4,5),B是對X軸鏡射的矩陣,C=A^-1,則ABCR=R',R'上面的數字為r'的x座標下面的數字為r'的y座標,則新座標r'為(1830,3374) (4)如果A是逆時針旋轉θ的矩陣,B是對X軸鏡射的矩陣,C=A^-1,ABCR=R',則對於任何θ,R'=R (5)如果A是逆時針旋轉60°的矩陣,B是對X軸鏡射的矩陣,C=A^-1,則ABCR=R',R'上面的數字為r'的x座標下面的數字為r'的y座標,則新座標r'為(-57+257√3,57√3+257)
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