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MatritsalarChiziqli algebraOliygoh≈ 0:49

[[1,2,3],[0,1,4],[5,6,0]] ning teskari matritsasi

Animatsion bosqichma-bosqich dars. Har bir qadamni subtitrlar bilan ko‘rish uchun Ijro tugmasini bosing yoki quyidagi qadamlar va matnni o‘qing. Javob: A⁻¹ = [[-24, 18, 5], [20, -15, -4], [-5, 4, 1]].

Yozib olingan video: ovoz va tasvirdagi yozuvlar ingliz tilida. Subtitrlar: Oʻzbekcha. Ushbu tildagi sharhlar uchun interaktiv versiyani oching.

Ingliz tilidagi video: MP4 faylini yuklab olish (0.3 MB) · Subtitrlar (WebVTT): Oʻzbekcha · Ingliz tilidagi subtitrlar (WebVTT)

Ekrandagi qadamlar

  1. 1. Masala
    Yechilgan misol
    [123014560]−1\begin{bmatrix}1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0\end{bmatrix}^{-1}
  2. 2. Qadamlar, 1-qism
    1. det⁡A=1≠0\det A = 1 \neq 0
      Determinant noldan farqli ekanini tekshirish
    2. [123100014010560001]\begin{bmatrix}1 & 2 & 3 & 1 & 0 & 0 \\ 0 & 1 & 4 & 0 & 1 & 0 \\ 5 & 6 & 0 & 0 & 0 & 1\end{bmatrix}
      Kengaytirilgan matritsani yozish [A | I]
    3. R3→R3−5R1: [1231000140100−4−15−501]R_{3} \to R_{3} - 5R_{1}:\ \begin{bmatrix}1 & 2 & 3 & 1 & 0 & 0 \\ 0 & 1 & 4 & 0 & 1 & 0 \\ 0 & -4 & -15 & -5 & 0 & 1\end{bmatrix}
      R1 dagi yetakchi element yordamida 1-ustunni tozalang
    4. R1→R1−2R2, R3→R3+4R2: [10−51−20014010001−541]R_{1} \to R_{1} - 2R_{2},\ R_{3} \to R_{3} + 4R_{2}:\ \begin{bmatrix}1 & 0 & -5 & 1 & -2 & 0 \\ 0 & 1 & 4 & 0 & 1 & 0 \\ 0 & 0 & 1 & -5 & 4 & 1\end{bmatrix}
      R2 dagi yetakchi element yordamida 2-ustunni tozalang
  3. 3. Qadamlar, 2-qism
    1. R1→R1+5R3, R2→R2−4R3: [100−2418501020−15−4001−541]R_{1} \to R_{1} + 5R_{3},\ R_{2} \to R_{2} - 4R_{3}:\ \begin{bmatrix}1 & 0 & 0 & -24 & 18 & 5 \\ 0 & 1 & 0 & 20 & -15 & -4 \\ 0 & 0 & 1 & -5 & 4 & 1\end{bmatrix}
      R3 dagi yetakchi element yordamida 3-ustunni tozalang
    2. A−1=[−2418520−15−4−541]A^{-1} = \begin{bmatrix}-24 & 18 & 5 \\ 20 & -15 & -4 \\ -5 & 4 & 1\end{bmatrix}
      Oʻng yarmi endi teskari matritsa
    3. AA−1=[100010001]A A^{-1} = \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}
      Tekshiruv: A·A⁻¹ = I
  4. 4. Javob
    A−1=[−2418520−15−4−541]A^{-1} = \begin{bmatrix}-24 & 18 & 5 \\ 20 & -15 & -4 \\ -5 & 4 & 1\end{bmatrix}

    A⁻¹ = [[-24, 18, 5], [20, -15, -4], [-5, 4, 1]]

  5. 5. Tekshirish
    • A ni natijaga koʻpaytirish aynan birlik matritsani beradi.

Matn

Masala. Mana masala: [[1,2,3],[0,1,4],[5,6,0]] ning teskari matritsasi. 3 karra 3 matritsaning teskarisini toping.

Qadamlar, 1-qism. Determinant noldan farqli ekanini tekshirish. Kengaytirilgan matritsani yozish [A | I]. R1 dagi yetakchi element yordamida 1-ustunni tozalang. R2 dagi yetakchi element yordamida 2-ustunni tozalang.

Qadamlar, 2-qism. R3 dagi yetakchi element yordamida 3-ustunni tozalang. Oʻng yarmi endi teskari matritsa. Tekshiruv: A karra A minus 1-darajasi teng I.

Javob. Demak, javob: A minus 1-darajasi teng [[-24, 18, 5], [20, minus 15, minus 4], [-5, 4, 1]]. Determinant 1, shuning uchun A teskarilanuvchi. Teskari matritsaning har bir elementi aniq.

Tekshirish. A ni natijaga koʻpaytirish aynan birlik matritsani beradi.

O‘xshash darslar

[[1,2,3],[0,1,4],[5,6,0]] ning teskari matritsasi — bosqichma-bosqich video dars