Question

perform each operation. place the answers in numerical order using the first element of each matrix.
a = (-1, 4)(5, -3) b = (-2, 5)(1, 3) c = (5, -4)(6, -2)
source
-2a
4b
c - a
2c
target

Explanation:

Step1: Calculate -2A

Matrix \( A =

$$\begin{pmatrix}-1 & 4 \\ 5 & -3\end{pmatrix}$$

\). To find \(-2A\), multiply each element by -2:

$$ -2A = -2
LATEXBLOCK1
=
LATEXBLOCK2
=
LATEXBLOCK3
$$

First element: \( 2 \)

Step2: Calculate 4B

Matrix \( B =

$$\begin{pmatrix}-2 & 5 \\ 1 & 3\end{pmatrix}$$

\). To find \(4B\), multiply each element by 4:

$$ 4B = 4
LATEXBLOCK5
=
LATEXBLOCK6
=
LATEXBLOCK7
$$

First element: \( -8 \)

Step3: Calculate \( C - A \)

Matrix \( C =

$$\begin{pmatrix}5 & -4 \\ 6 & -2\end{pmatrix}$$

\), Matrix \( A =

$$\begin{pmatrix}-1 & 4 \\ 5 & -3\end{pmatrix}$$

\). Subtract corresponding elements:

$$ C - A =
LATEXBLOCK10
=
LATEXBLOCK11
$$

First element: \( 6 \)

Step4: Calculate 2C

Matrix \( C =

$$\begin{pmatrix}5 & -4 \\ 6 & -2\end{pmatrix}$$

\). To find \(2C\), multiply each element by 2:

$$ 2C = 2
LATEXBLOCK13
=
LATEXBLOCK14
=
LATEXBLOCK15
$$

First element: \( 10 \)

Now, list the first elements: \( -8 \) (from 4B), \( 2 \) (from -2A), \( 6 \) (from \( C - A \)), \( 10 \) (from 2C). Order them numerically: \( -8, 2, 6, 10 \)

Answer:

The first elements in numerical order are \(-8\) (from \(4B\)), \(2\) (from \(-2A\)), \(6\) (from \(C - A\)), \(10\) (from \(2C\)). So the ordered operations by first element are \(4B\), \(-2A\), \(C - A\), \(2C\)