Question

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Answer 1

Step-by-step explanation:

Given:

$A=\left[\begin{array}{cc}2&-1\\-4&5\end{array}\right],$$B=\left[\begin{array}{cc}0&-3\end{array}\right]$

To find: If CA=B

1) Write the order of C.

2) Find the matrix C.

Solution:

1) Write the order of C:

We know that in matrix multiplication column of first matrix is equal to row of second matrix.

In CA

Column of matrix C is equal to row of matrix A.

Here,we must keep in mind that CA=B

order of B is 1×2 and order of A is 2×2

Thus,

Order of C is 1×2

2)Find the matrix C:

let matrix C is

$C=\left[\begin{array}{cc}x&y\end{array}\right]$

put the values of C, A and B into given eq

CA=B

$\left[\begin{array}{cc}x&y\end{array}\right]\times\left[\begin{array}{cc}2&-1\\-4&5\end{array}\right]=\left[\begin{array}{cc}0&-3\end{array}\right]$

Multiply both matrix in LHS

$\left[\begin{array}{cc}2x-4y&-x+5y\end{array}\right]=\left[\begin{array}{cc}0&-3\end{array}\right]$

Equate both matrix

$2x - 4y = 0 \: \: ...eq1\\ \\ - x + 5y = - 3 \: \: ...eq2$

take common 2 from eq1 and add both eqs

$x - 2y = 0 \\ - x + 5y = - 3 \\ - - - - - - - \\ 3y = - 3 \\ \\ y = - 1$

put the value of y in eq1

$x - 2( - 1) = 0 \\ \\ x + 2 = 0 \\ \\ x = - 2$

Thus,

Matrix C is

$C=\left[\begin{array}{cc}-2&-1\end{array}\right]$

Final answer:

1) Order of C is [1×2].

2)Matrix C is

$C=\left[\begin{array}{cc}-2&-1\end{array}\right]$

Hope it helps you.

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