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julsineya [31]
4 years ago
12

Let Aequals=[Start 2 By 2 Matrix 1st Row 1st Column 4 2nd Column 2 2nd Row 1st Column negative 1 2nd Column 2 EndMatrix ]4 2 −1

2 and Bequals=[Start 2 By 2 Matrix 1st Row 1st Column 2 2nd Column 4 2nd Row 1st Column negative 2 2nd Column k EndMatrix ]2 4 −2 k . What​ value(s) of​ k, if​ any, will make ABequals=​BA?
Mathematics
1 answer:
7nadin3 [17]4 years ago
7 0

Answer:

k=-2

Step-by-step explanation:

Given matrix

A=\left[\begin{array}{ccc}4&2\\-1&2\end{array}\right]

And

B=\left[\begin{array}{ccc}2&4\\-2&k\end{array}\right]

We need to find the value of k, that will make AB=BA.

Let us find AB

AB=\left[\begin{array}{ccc}4&2\\-1&2\end{array}\right]\times \left[\begin{array}{ccc}2&4\\-2&k\end{array}\right]

AB=\left[\begin{array}{ccc}4&16+2k\\-6&-4+2k\end{array}\right]

Now, let us find BA

BA=\left[\begin{array}{ccc}2&4\\-2&k\end{array}\right]\times \left[\begin{array}{ccc}4&2\\-1&2\end{array}\right]

BA=\left[\begin{array}{ccc}4&12\\-8-k&-4+2k\end{array}\right]

Put AB=BA

\left[\begin{array}{ccc}4&16+2k\\-6&-4+2k\end{array}\right]=\left[\begin{array}{ccc}4&12\\-8-k&-4+2k\end{array}\right]

In order to make AB=BA, the 16+2k=12\ and\ -6=-8-k should be equal. As other two values are equal that are 4\ and -4+2k

By solving each equation

16+2k=12\\2k=-4\\k=-2

And

-6=-8-k\\-k=-6+8\\k=-2

We can see if the value k=-2 then AB=BA

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<em>Hi there ! </em>

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