"Solve [6−59−4−53]=2X−5[21−6−663]" was answered by our experts

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Chesley

Answered question

2021-01-31

Solve $[\begin{matrix} 6 & - 5 & 9 \\ - 4 & - 5 & 3 \end{matrix}] = 2 X - 5 [\begin{matrix} 2 & 1 & - 6 \\ - 6 & 6 & 3 \end{matrix}]$

Answer & Explanation

2abehn

Skilled2021-02-01Added 88 answers

Step 1
Matrix addition and subtraction are same like adding and subtracting the given two numbers
Addition and subtraction is done with the same entries of the given two matrices
For example, if A and B are two matrices then addition is done as follows,
$A = [\begin{matrix} a & b \\ c & d \end{matrix}] and B = [\begin{matrix} e & f \\ g & h \end{matrix}] Then, A + B = [\begin{matrix} a + e & b + f \\ c + g & d + h \end{matrix}]$
Step 2
Now given,
$[\begin{matrix} 6 & - 5 & 9 \\ - 4 & - 5 & 3 \end{matrix}] = 2 X - 5 [\begin{matrix} 2 & 1 & - 6 \\ - 6 & 6 & 3 \end{matrix}]$

$[\begin{matrix} 6 & - 5 & 9 \\ - 4 & - 5 & 3 \end{matrix}] = 2 X - [\begin{matrix} 10 & 5 & - 30 \\ - 30 & 30 & 15 \end{matrix}] 2 X = [\begin{matrix} 6 & - 5 & 9 \\ - 4 & - 5 & 3 \end{matrix}] + [\begin{matrix} 10 & 5 & - 30 \\ - 30 & 30 & 15 \end{matrix}] 2 X = [\begin{matrix} 16 & 0 & - 21 \\ - 34 & 25 & 18 \end{matrix}] X = \frac{1}{2} [\begin{matrix} 16 & 0 & - 21 \\ - 34 & 25 & 18 \end{matrix}]$

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