QuestionDiberikan $M=K+L^{\mathrm{T}}$ , cari nilai $y$ yang memenuhi dengan $K=\begin{pmatrix}5 & x+1 \\ 2 & y-x\end{pmatrix}$ dan $L=\begin{pmatrix}4 & 5 \\ 2x-1 & 3x+y\end{pmatrix}$ . Pilihan: a. -4, b. -3, c. -2, d. 3, e. 4.

Studdy Solution

STEP 1

Assumptions1. We have matrix $K=\left(\begin{array}{ll}5 & x+1 \\ & y-x\end{array}\right)$ . We have matrix $=\left(\begin{array}{cc}4 &5 \\ x-1 &3 x+y\end{array}\right)$ 3. We have matrix $M=\left(\begin{array}{cc}9 &12 \\7 &\end{array}\right)$ 4. We know that $M=K+^{\mathrm{T}}$ , where $^{\mathrm{T}}$ is the transpose of matrix $$
5. We need to find the value of $y$ that satisfies the equation $M=K+^{\mathrm{T}}$

STEP 2

First, we need to find the transpose of matrix $$. The transpose of a matrix is obtained by interchanging its rows into columns or vice versa.
$^{\mathrm{T}} = \left(\begin{array}{cc}4 &2 x-1 \\5 & x+y\end{array}\right)$

STEP 3

Now, we can add matrix $K$ and $^{\mathrm{T}}$ to get matrix $M$ .
$M = K + L^{\mathrm{T}}$ $\left(\begin{array}{cc}9 &12 \\7 &2\end{array}\right) = \left(\begin{array}{ll}5 & x+1 \\2 & y-x\end{array}\right) + \left(\begin{array}{cc} &2 x-1 \\5 &3 x+y\end{array}\right)$

STEP 4

We can equate the corresponding elements of the matrices on both sides of the equation.
$+4 =9, x+1 +2x-1 =12,2 + =7, y-x +3x+y =2$

STEP 5

olving the equations, we get $x =3, y = -2$ So, the value of $y$ that satisfies the equation is -2.

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