If A= [ cc 2 & a -3 & 5 ] and B= [ cc -2 & 3 7 & b ], C= [ cc c & 9 -1 & -11 ] and 5 A+2 B=C, find the values of a, b, c

& A = [ cc 2 & a -3 & 5 ] and B = [ cc -2 & 3 7 & b ], C = [ cc c & 9 -1 & -11 ] and 5 A +2 B = C & 5 [ cc 2 & a -3 & 5 ]+2 [ cc -2 & 3 7 & b ]= [ cc c & 9 -1 & -11 ] & [ cc 10 & 5 a -15 & 25 ]+ [ cc -4 & 6 14 & 2 b ]= [ cc c & 9 -1 & -11 ] & [ cc 10-4 & 5 a+6 15+14 & 25+2 b ]= [ cc c & 9 -1 & -11 ] & [ cc 6 & 5 a+6 -1 & 25+2 b ]= [ cc c & 9 -1 & -11 ] Comparing each term & 5 a+6=9 & 5 a=9-6=3 & a=3 5 & 25+2 b=-11 & 2 b=-11-25=-36 & b=-36 2 =-18 & c=6 Hence a=3 5 , b=-18 and c=6.

If A= [ cc 2 & a -3 & 5 ] and B= [ cc -2 & 3 7 & b ], C= [ cc c &…

Download App

Question

If $A=\left[\begin{array}{cc}2 & a \\ -3 & 5\end{array}\right]$ and $B=\left[\begin{array}{cc}-2 & 3 \\ 7 & b\end{array}\right], C=\left[\begin{array}{cc}c & 9 \\ -1 & -11\end{array}\right]$ and $5 A+2 B=C$, find the values of $a, b, c$

✓

Answer

$
\begin{aligned}
& A =\left[\begin{array}{cc}
2 & a \\
-3 & 5
\end{array}\right] \text { and } B =\left[\begin{array}{cc}
-2 & 3 \\
7 & b
\end{array}\right], C =\left[\begin{array}{cc}
c & 9 \\
-1 & -11
\end{array}\right] \text { and } 5 A +2 B = C \\
& \Rightarrow 5\left[\begin{array}{cc}
2 & a \\
-3 & 5
\end{array}\right]+2\left[\begin{array}{cc}
-2 & 3 \\
7 & b
\end{array}\right]=\left[\begin{array}{cc}
c & 9 \\
-1 & -11
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{cc}
10 & 5 a \\
-15 & 25
\end{array}\right]+\left[\begin{array}{cc}
-4 & 6 \\
14 & 2 b
\end{array}\right]=\left[\begin{array}{cc}
c & 9 \\
-1 & -11
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{cc}
10-4 & 5 a+6 \\
15+14 & 25+2 b
\end{array}\right]=\left[\begin{array}{cc}
c & 9 \\
-1 & -11
\end{array}\right] \\
& \Rightarrow\left[\begin{array}{cc}
6 & 5 a+6 \\
-1 & 25+2 b
\end{array}\right]=\left[\begin{array}{cc}
c & 9 \\
-1 & -11
\end{array}\right]
\end{aligned}
$
Comparing each term
$
\begin{aligned}
& 5 a+6=9 \\
& \Rightarrow 5 a=9-6=3 \\
& \Rightarrow a=\frac{3}{5} \\
& \Rightarrow 25+2 b=-11 \\
& \Rightarrow 2 b=-11-25=-36 \\
& \Rightarrow b=-\frac{36}{2}=-18 \\
& c=6
\end{aligned}
$
Hence $a=\frac{3}{5}, b=-18$ and $c=6$.