Question

Let 'A' be a matrix such that [1,0]A = [1,2,0] and [0,1]A = [0,-1,1]. Then find the product matrix
-1
A 1 = ?
1

Answer 1

@tkhunny see what I mean?

Answer 2

sorry electrokid i didnt get u...

Answer 3

@soumyan dont worry man.

Answer 4

k i wil wait....

Answer 5

i am not man, me a girl....

Answer 6

\(\left[\begin{matrix}1&0\end{matrix}\right]A=\left[\begin{matrix}1&2&0\end{matrix}\right]\) and \(\left[\begin{matrix}0&1\end{matrix}\right]A=\left[\begin{matrix}0&-1&1\end{matrix}\right]\)?

For matrix multiplication to be defined, the number of columns of the first matrix must match with the number of rows of the second matrix, and the product matrix has dimensions (number of rows of first matrix)\(\times\)(number of columns of second matrix).

So, you know that matrix \(A\) has dimensions 2\(\times\)3.

Let \(A=\left[\begin{matrix}a&b&c\\d&e&f\end{matrix}\right].\)

Now, you have
\[\left[\begin{matrix}1&0\end{matrix}\right]\left[\begin{matrix}a&b&c\\d&e&f\end{matrix}\right]=\left[\begin{matrix}1&2&0\end{matrix}\right]\\
\left[\begin{matrix}a&b&c\end{matrix}\right]=\left[\begin{matrix}1&2&0\end{matrix}\right]\]
and
\[\left[\begin{matrix}0&1\end{matrix}\right]\left[\begin{matrix}a&b&c\\d&e&f\end{matrix}\right]=\left[\begin{matrix}0&-1&1\end{matrix}\right]\\
\left[\begin{matrix}d&e&f\end{matrix}\right]=\left[\begin{matrix}0&-1&1\end{matrix}\right]\]

Answer 7

Now, you know what \(A\) is, so you just multiply it by\(\left[\begin{matrix}-1\\1\\1\end{matrix}\right].\)

Answer 8

thanks mr. sithsandgiggles......