10. UTBK/PREDIKSI TPS/PK/2024 Jika matriks A=(} 1&4 2&3 maka m-n=ldots . A. -2 B. -1 C. o o E.

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10. UTBK/PREDIKSI TPS/PK/2024 Jika matriks A=(} 1&4 2&3 maka m-n=ldots . A. -2 B. -1 C. o o E.

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Answer 1

Here's how to solve the problem:

1. Find the square of matrix A:

* $A^2 = A \cdot A = \begin{pmatrix} 1 & 4 \\ 2 & 3 \end{pmatrix} \cdot \begin{pmatrix} 1 & 4 \\ 2 & 3 \end{pmatrix} = \begin{pmatrix} (1)(1)+(4)(2) & (1)(4)+(4)(3) \\ (2)(1)+(3)(2) & (2)(4)+(3)(3) \end{pmatrix} = \begin{pmatrix} 9 & 16 \\ 8 & 17 \end{pmatrix}$

2. Define the identity matrix:

* The identity matrix of order 2x2 is: $I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$

3. Substitute into the equation:

* The equation is: $mA + nI = A^2$
* Substitute the matrices: $m \begin{pmatrix} 1 & 4 \\ 2 & 3 \end{pmatrix} + n \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} = \begin{pmatrix} 9 & 16 \\ 8 & 17 \end{pmatrix}$

4. Simplify the equation:

* This gives us: $\begin{pmatrix} m+n & 4m \\ 2m & 3m+n \end{pmatrix} = \begin{pmatrix} 9 & 16 \\ 8 & 17 \end{pmatrix}$

5. Solve for m and n:

* By comparing corresponding elements, we get the following system of equations:
* m + n = 9
* 4m = 16
* 2m = 8
* 3m + n = 17

* Solving for m, we find m = 4.
* Substituting m = 4 into the first equation, we find n = 5.

6. Calculate m - n:

* m - n = 4 - 5 = -1

Therefore, the answer is B. -1

Pertanyaan

10. UTBK/PREDIKSI TPS/PK/2024 Jika matriks A=(} 1&4 2&3 maka m-n=ldots . A. -2 B. -1 C. o o E.

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