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cjgonzalez981
14.02.2020 •
Mathematics
The given matrix equation is false in general. Explain why the equation is false. Assume that all matrices are n ✕ n. (A + B)2 = A2 + 2AB + B2 (A + B)2 = A2 + AB + BA + B2. This is only equal to A2 + 2AB + B2 when AB = −BA, which in general is not true. (A + B)2 = A2 + AB − AB + B2 = A2 + B2. This is only equal to A2 + 2AB + B2 when A = 0nn or B = 0nn, which in general is not true. (A + B)2 = A2 − BA + BA + B2 = A2 + B2. This is only equal to A2 + 2AB + B2 when A = 0nn or B = 0nn, which in general is not true. (A + B)2 = A2 + AB + BA + B2. This is only equal to A2 + 2AB + B2 when AB = BA, which in general is not true. Give a 2 ✕ 2 example showing the equation is false. A = 1 2 3 4
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Ответ:
Fourth option is the correct one.
Step-by-step explanation:
Given:
Lets Assume
Now,
if we multiply both in sequence AB, we get
Now if we multiply both in sequence BA, we get
=![\left[\begin{array}{ccc}4.1+0.3&4.2+0.4\\0.1+1.3&0.2+1.4\end{array}\right]](/tpl/images/0512/0261/49d99.png)
Hence AB ≠ BA
Now according to equation,
(A+B)² = A² + B² + AB + BA = A² + B² + 2AB only when AB = BA which is not the case as seen in example above
Ответ: