m x H = [tex]\left[\begin{array}{ccc}-25&37.5&-12.5\\\9\end{array}\right][/tex]
Step-by-step explanation:
Step 1; Multiply 5 with this matrix [tex]\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right][/tex] and we get a matrix [tex]\left[\begin{array}{ccc}-5&10\\20&40\\\end{array}\right][/tex]
Multiply the fraction [tex]\frac{2}{5}[/tex] with the matrix [tex]\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right][/tex] and we get [tex]\left[\begin{array}{ccc}-\frac{2m}{5} &\frac{4m}{5} \\\frac{8m}{5} &\frac{16m}{5} \\\end{array}\right][/tex]
Step2; Now equate corresponding values of the matrices with each other.
-5 = [tex]\frac{-2m}{5}[/tex] and so on. By equating we get the value of m as [tex]\frac{25}{2}[/tex]
Step 3; Add the matrices to get the value of matrix m.
Adding the three matrices on the RHS we get [tex]\left[\begin{array}{ccc}2&9&-9\\\end{array}\right][/tex].
Step 4; Adding the matrices on the LHS we get the resulting matrix as H +
[tex]\left[\begin{array}{ccc}4&6&-8\\\9\end{array}\right][/tex]. Equating the matrices from step 3 and 4 we get the value of H as [tex]\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right][/tex]
Step 5; Now to find the value of m x H we need to multiply the value of [tex]\frac{25}{2}[/tex] with the matrix [tex]\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right][/tex]
Step 6; Multiplying we get the matrix m x H = [ -25 [tex]\frac{75}{2}[/tex] [tex]\frac{-25}{2}[/tex] ]
