Math

QuestionFind the matrix CC given A=[75106]A=\begin{bmatrix}7 & -5 \\ 10 & 6\end{bmatrix} and B=[621814]B=\begin{bmatrix}6 & 2 \\ -18 & 14\end{bmatrix}, where C=2ABC=-2A-B.

Studdy Solution

STEP 1

Assumptions1. Matrix A=[75106]A=\left[\begin{array}{cc}7 & -5 \\10 &6\end{array}\right] . Matrix B=[61814]B=\left[\begin{array}{cc}6 & \\ -18 &14\end{array}\right]
3. We need to find the matrix C=ABC=- A-B

STEP 2

First, we need to calculate 2A-2A. This can be done by multiplying each element of matrix AA by -2.
2A=2×[75106]-2A = -2 \times \left[\begin{array}{cc}7 & -5 \\10 &6\end{array}\right]

STEP 3

Perform the multiplication operation on each element of matrix AA.
2A=[2×72×52×102×6]-2A = \left[\begin{array}{cc}-2 \times7 & -2 \times -5 \\ -2 \times10 & -2 \times6\end{array}\right]

STEP 4

Calculate the result of the multiplication.
2A=[14102012]-2A = \left[\begin{array}{cc}-14 &10 \\ -20 & -12\end{array}\right]

STEP 5

Now, we need to subtract matrix BB from 2A-2A to get matrix CC.
C=2AB=[14102012][21814]C = -2A - B = \left[\begin{array}{cc}-14 &10 \\ -20 & -12\end{array}\right] - \left[\begin{array}{cc} &2 \\ -18 &14\end{array}\right]

STEP 6

Perform the subtraction operation on each corresponding element of the two matrices.
C=[14610220(18)1214]C = \left[\begin{array}{cc}-14-6 &10-2 \\ -20-(-18) & -12-14\end{array}\right]

STEP 7

Calculate the result of the subtraction.
C=[20226]C = \left[\begin{array}{cc}-20 & \\2 & -26\end{array}\right]So, the matrix C=2ABC=-2 A-B is [20226]\left[\begin{array}{cc}-20 & \\2 & -26\end{array}\right].

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