Question

[tex] Find a and b, if 2\left[\begin{array}{ccc}5&a\\3&4\end{array}\right] +\left[\begin{array}{ccc}0&1\\1&b\end{array}\right] =\left[\begin{array}{ccc}10&5\\7&0\end{array}\right] [\tex]

Answer 1

Answer:

a=2 and b= -8

Step-by-step explanation:

$2\left[\begin{array}{ccc}5&a\\3&4\end{array}\right] +\left[\begin{array}{ccc}0&1\\1&b\end{array}\right] =\left[\begin{array}{ccc}10&5\\7&0\end{array}\right] [\tex]\\\left[\begin{array}{ccc}10&2a\\6&8\end{array}\right] +\left[\begin{array}{ccc}0&1\\1&b\end{array}\right] =\left[\begin{array}{ccc}10&5\\7&0\end{array}\right] [\tex]\\\left[\begin{array}{ccc}10&2a+1\\7&8+b\end{array}\right] =\left[\begin{array}{ccc}10&5\\7&0\end{array}\right] [\tex]\\\\hence by comaparing the terms of matrix\\2a+1=5\\2a=4$

a=2

and 8+b=0

b=-8

Answer 2

Answer:

a = 2 and b = -8

Step-by-step explanation:

$2\left[\begin{array}{ccc}5&a\\3&4\end{array}\right] +\left[\begin{array}{ccc}0&1\\1&b\end{array}\right] =\left[\begin{array}{ccc}10&5\\7&0\end{array}\right]$

⇒$\left[\begin{array}{ccc}10&2a\\6&8\end{array}\right] +\left[\begin{array}{ccc}0&1\\1&b\end{array}\right] =\left[\begin{array}{ccc}10&5\\7&0\end{array}\right]$

⇒$\left[\begin{array}{ccc}10&\left ( 2a+1 \right )\\7&\left ( 8+b \right )\end{array}\right] =\left[\begin{array}{ccc}10&5\\7&0\end{array}\right]$

By comparing LHS matrix to RHS matrix ,we get:

      2a+1 = 5        and         8+b = 0

     ⇒ 2a = 4                     ⇒ b = -8                    

     ⇒ a = 2