Diketahui matriks A=[x+y x y x-y], B=[1 -1/2x -2y 3], dan A^T=B dengan AT menyatakan transpose da...

Summary

The script discusses solving a matrix equation by transposing known values. It explains how to rearrange matrix elements and solve for variables x and y using equations x+y=1 and x-y=3. The process involves elimination to find y=-1, then substituting back to find x=2. Finally, it calculates x+2y, resulting in 0, concluding the solution.

Takeaways

• 📝 A transpose is equivalent to matrix B in the given problem.
• 🔄 Transposing matrix A involves changing rows into columns or vice versa.
• 🧮 The problem begins by converting A transpose: first row becomes a column.
• ➕ Equation 1: x + y is given, with x turned into a column form.
• ✖️ Equation 2: x - y equals 3, which is another equation to solve.
• ⚙️ Solving the system of equations by substitution: x = -2y.
• ➗ By elimination, 2y equals 1, solving for y gives y = -1.
• 🔢 Substituting y back gives x = 2 from the equation x = -2y.
• ➖ Finally, x + 2y is calculated as 2 + 2*(-1), which equals 0.
• ✅ The answer to the problem is option C: 0.

Q & A

What is the first step in solving the problem involving matrix A and B?

The first step is to transpose matrix A by converting a row into a column, or vice versa, based on the provided values of A.

How do you transpose matrix A in the given example?

Matrix A is transposed by changing the row [x, y] into a column, where x is placed in the first row and y in the second row.

What equation do we derive from comparing A transpose with matrix B?

From comparing A transpose with matrix B, we derive the equation x = -2y.

What are the two main equations used for solving this problem?

The two main equations are x + y = 1 and x - y = 3.

How is the elimination method applied to solve the system of equations?

The elimination method is applied by subtracting x - y = 3 from x + y = 1, which eliminates x and gives 2y = -2, solving for y.

What is the value of y after solving the equation?

The value of y is -1.

How is the value of x determined after finding y?

The value of x is determined by substituting y = -1 into the equation x = -2y, resulting in x = 2.

What is the expression for x + 2y, and how is it calculated?

The expression for x + 2y is calculated as 2 + 2(-1) = 2 - 2 = 0.

What is the final answer to the problem?

The final answer to the problem is 0, which corresponds to option C.

How is the elimination method useful in this type of problem?

The elimination method simplifies solving systems of equations by removing one variable, making it easier to solve for the other variable.