Math Problem Statement
How many nonzero elements are in the matrix below?
Matrix:
[ [2, 0, 0, 3.1, 22, 9],
[0, 21, 3.2, 0, 0, 6],
[1, 42, 0, 0, 8, 0],
[40, 0, 0, 4, 6, 14],
[10, 20, 0, 13, 5, 6.3] ]
Answer choices:
- 11
- 16
- 19
- 30
Solution
To solve this problem, we need to count the number of nonzero elements in the matrix.
Matrix Analysis
Here’s the matrix provided in the image:
2 & 0 & 0 & 3.1 & 22 & 9 \\ 0 & 21 & 3.2 & 0 & 0 & 6 \\ 1 & 42 & 0 & 0 & 8 & 0 \\ 40 & 0 & 0 & 4 & 6 & 14 \\ 10 & 20 & 0 & 13 & 5 & 6.3 \\ \end{bmatrix}$$ ### Counting Nonzero Elements Let's go through each row and count the nonzero entries: 1. **Row 1**: $$2, 3.1, 22, 9$$ → 4 nonzero elements 2. **Row 2**: $$21, 3.2, 6$$ → 3 nonzero elements 3. **Row 3**: $$1, 42, 8$$ → 3 nonzero elements 4. **Row 4**: $$40, 4, 6, 14$$ → 4 nonzero elements 5. **Row 5**: $$10, 20, 13, 5, 6.3$$ → 5 nonzero elements Adding them up: $$4 + 3 + 3 + 4 + 5 = 19$$ ### Answer The correct answer is **19**. Would you like further details on matrix concepts or have any questions? --- Here are 5 related questions to explore further: 1. How can we represent the sparsity of a matrix? 2. What are the benefits of sparse matrices in computation? 3. How do we determine if a matrix is sparse or dense? 4. What techniques exist to store sparse matrices efficiently? 5. How can we identify and count nonzero elements programmatically? **Tip:** When working with matrices, practice identifying patterns in nonzero entries, as this can simplify complex calculations.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Matrix analysis
Counting nonzero elements
Formulas
Counting of nonzero elements in a matrix
Theorems
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Suitable Grade Level
Grades 9-12