Given the matrices A and B shown below , solve for X in the equation −13X+12A=B A=[−10488],B=[9−142]

Step 1 the given matrices are: A=[−10488],B=[9−142] we have to solve for X in the equation −13X+12A=B Step 2 the given matrices are: A=[−10488] and B=[9−142] −13X+12A=B −13X+12[−10488]=[9−142] −13X+[−102428282]=[9−142] −13X+[−5244]=[9−142] −13X=[9−142]−[−5244] −13X=[9−142]+[5−2−4−4] −13X=[9+5−1−24−42−4] −13X=[14−30−2] X=−3[14−30−2] X=[14×(−3)−3×(−3)0×(−3)−2×(−3)] X=[−42906] Step 3 therefore the matrix X is [−42906] therefore the solution of X for the equation −13X+12A=B is X=[−42906]

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Lennie Carroll Answered2020-12-09

Given the matrices A and B shown below , solve for X in the equation

- \frac{1}{3} X + \frac{1}{2} A = B

A = [\begin{matrix} - 10 & 4 \\ 8 & 8 \end{matrix}], B = [\begin{matrix} 9 & - 1 \\ 4 & 2 \end{matrix}]

Answer & Explanation

StrycharzT

Expert

2020-12-10Added 102 answers

Step 1
the given matrices are:

A = [\begin{matrix} - 10 & 4 \\ 8 & 8 \end{matrix}], B = [\begin{matrix} 9 & - 1 \\ 4 & 2 \end{matrix}]

we have to solve for X in the equation

- \frac{1}{3} X + \frac{1}{2} A = B

Step 2
the given matrices are:

A = [\begin{matrix} - 10 & 4 \\ 8 & 8 \end{matrix}] and B = [\begin{matrix} 9 & - 1 \\ 4 & 2 \end{matrix}]

- \frac{1}{3} X + \frac{1}{2} A = B

\frac{- 1}{3} X + \frac{1}{2} [\begin{matrix} - 10 & 4 \\ 8 & 8 \end{matrix}] = [\begin{matrix} 9 & - 1 \\ 4 & 2 \end{matrix}]

\frac{- 1}{3} X + [\begin{matrix} - \frac{10}{2} & \frac{4}{2} \\ \frac{8}{2} & \frac{8}{2} \end{matrix}] = [\begin{matrix} 9 & - 1 \\ 4 & 2 \end{matrix}]

\frac{- 1}{3} X + [\begin{matrix} - 5 & 2 \\ 4 & 4 \end{matrix}] = [\begin{matrix} 9 & - 1 \\ 4 & 2 \end{matrix}]

\frac{- 1}{3} X = [\begin{matrix} 9 & - 1 \\ 4 & 2 \end{matrix}] - [\begin{matrix} - 5 & 2 \\ 4 & 4 \end{matrix}]

\frac{- 1}{3} X = [\begin{matrix} 9 & - 1 \\ 4 & 2 \end{matrix}] + [\begin{matrix} 5 & - 2 \\ - 4 & - 4 \end{matrix}]

\frac{- 1}{3} X = [\begin{matrix} 9 + 5 & - 1 - 2 \\ 4 - 4 & 2 - 4 \end{matrix}]

\frac{- 1}{3} X = [\begin{matrix} 14 & - 3 \\ 0 & - 2 \end{matrix}]

X = - 3 [\begin{matrix} 14 & - 3 \\ 0 & - 2 \end{matrix}]

X = [\begin{matrix} 14 \times (- 3) & - 3 \times (- 3) \\ 0 \times (- 3) & - 2 \times (- 3) \end{matrix}]

X = [\begin{matrix} - 42 & 9 \\ 0 & 6 \end{matrix}]

Step 3
therefore the matrix X is

[\begin{matrix} - 42 & 9 \\ 0 & 6 \end{matrix}]

therefore the solution of X for the equation

- \frac{1}{3} X + \frac{1}{2} A = B is X = [\begin{matrix} - 42 & 9 \\ 0 & 6 \end{matrix}]

Jeffrey Jordon

Expert

2022-01-29Added 2575 answers

Answer is given below (on video)

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