Math Problem Statement
Determine matrix A, where A is given as the 3x3 matrix:
[[-5, 3, 8], [0, 1, 8], [7, 2, 9]].
Solution
The image contains a matrix-related problem in which matrix is given as:
-5 & 3 & 8 \\ 0 & 1 & 8 \\ 7 & 2 & 9 \end{pmatrix}$$ The task appears to be finding the determinant of matrix $$A$$, which is written as "tentukan matriks A", meaning "determine matrix A". In this context, "determine" usually implies finding the determinant of matrix $$A$$. ### Step-by-step solution for the determinant: For a 3x3 matrix, the determinant $$\text{det}(A)$$ can be calculated using the following formula: $$\text{det}(A) = a(ei - fh) - b(di - fg) + c(dh - eg)$$ Where the matrix $$A$$ is: $$A = \begin{pmatrix} a & b & c \\ d & e & f \\ g & h & i \end{pmatrix}$$ For matrix $$A$$: $$A = \begin{pmatrix} -5 & 3 & 8 \\ 0 & 1 & 8 \\ 7 & 2 & 9 \end{pmatrix}$$ - $$a = -5$$, $$b = 3$$, $$c = 8$$ - $$d = 0$$, $$e = 1$$, $$f = 8$$ - $$g = 7$$, $$h = 2$$, $$i = 9$$ Now, substitute the values into the determinant formula: $$\text{det}(A) = -5(1 \cdot 9 - 8 \cdot 2) - 3(0 \cdot 9 - 8 \cdot 7) + 8(0 \cdot 2 - 1 \cdot 7)$$ Simplifying each part: $$\text{det}(A) = -5(9 - 16) - 3(0 - 56) + 8(0 - 7)$$ $$= -5(-7) - 3(-56) + 8(-7)$$ $$= 35 + 168 - 56$$ $$\text{det}(A) = 147$$ Thus, the determinant of matrix $$A$$ is: $$\boxed{147}$$ Let me know if you'd like more details on any step or further clarification! Here are some related questions to deepen your understanding: 1. How would you find the inverse of a matrix using the determinant? 2. What does the determinant of a matrix signify geometrically? 3. How can the determinant be used to solve systems of linear equations? 4. What happens if the determinant of a matrix is zero? 5. Can you determine the determinant of a larger matrix (e.g., 4x4 or higher)? **Tip:** The determinant helps determine whether a matrix is invertible. If the determinant is zero, the matrix is singular and has no inverse!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix Algebra
Determinants
Linear Algebra
Formulas
det(A) = a(ei - fh) - b(di - fg) + c(dh - eg)
Theorems
Determinant Formula for 3x3 Matrices
Suitable Grade Level
Grades 10-12
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