Jika 3 * [[1/3], [1/3]] + 3 * [[3], [0], [2]] + k * [[2], [1], [3]] = [[2], [- 1], [1]] adalah maka k

A. -4

B. -2

C. 2

D. 3

Ε. 4

Diberikan persamaan matriks:

\[
3 \times \begin{bmatrix} \frac{1}{3} \\ \frac{1}{3} \end{bmatrix} + 3 \times \begin{bmatrix} 3 \\ 0 \\ 2 \end{bmatrix} + k \times \begin{bmatrix} 2 \\ 1 \\ 3 \end{bmatrix} = \begin{bmatrix} 2 \\ -1 \\ 1 \end{bmatrix}
\]

Langkah-langkah penyelesaian:

### 1. Mengalikan skalar dengan matriks:

\[
3 \times \begin{bmatrix} \frac{1}{3} \\ \frac{1}{3} \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \end{bmatrix}
\]

\[
3 \times \begin{bmatrix} 3 \\ 0 \\ 2 \end{bmatrix} = \begin{bmatrix} 9 \\ 0 \\ 6 \end{bmatrix}
\]

Matriks-matriks di atas memiliki ukuran berbeda, jadi kita dapat mengasumsikan bahwa kolom pertama memiliki dua entri, dan elemen-elemen yang hilang dianggap nol untuk baris ketiga. Jadi, kita tambahkan elemen nol untuk melengkapi operasi penjumlahan:

\[
\begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix} + \begin{bmatrix} 9 \\ 0 \\ 6 \

Jika 3 * [[1/3], [1/3]] + 3 * [[3], [0], [2]] + k * [[2], [1], [3]] = [[2], [-1], [1]] adalah maka k

A. -4

B. -2

C. 2

D. 3

Ε. 4

Learn how to solve for the variable k in a matrix equation involving scalar multiplication and matrix addition. This problem covers key concepts in matrix algebra, including scalar multiplication and matrix addition, and is suitable for students in Grades 10-12.

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