What is the resulting matrix when \(A = 4 & -3 2 & 0 \) is added to \(B = -1 & 5 -2 & 7 \)?

Mathematics

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Answer

[3207]\begin{bmatrix} 3 & 2 \\ 0 & 7 \end{bmatrix}

Step-by-step solution

4 steps

Ili kuongeza matriki mbili, tunaongeza vipengele vinavyolingana.

  1. Andika fomula ya kuongeza matriki.

    Ikiwa A=[abcd]A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} na B=[efgh]B = \begin{bmatrix} e & f \\ g & h \end{bmatrix}, basi A+B=[a+eb+fc+gd+h]A + B = \begin{bmatrix} a+e & b+f \\ c+g & d+h \end{bmatrix}.

  2. Badilisha matriki AA na BB kwenye fomula.

    A+B=[4−320]+[−15−27]A + B = \begin{bmatrix} 4 & -3 \\ 2 & 0 \end{bmatrix} + \begin{bmatrix} -1 & 5 \\ -2 & 7 \end{bmatrix}
  3. Fanya hesabu ya kila kipengele.

    A+B=[4+(−1)−3+52+(−2)0+7]A + B = \begin{bmatrix} 4 + (-1) & -3 + 5 \\ 2 + (-2) & 0 + 7 \end{bmatrix}
  4. Rahisisha vipengele ili kupata matriki inayotokana.

    A+B=[3207]A + B = \begin{bmatrix} 3 & 2 \\ 0 & 7 \end{bmatrix}

    Matriki inayotokana ni:

    [3207]\begin{bmatrix} 3 & 2 \\ 0 & 7 \end{bmatrix}
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