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Find if the matrix is a sparse matrixInput:  1 0 3             0 0 4             6 0 0Output: YesExplaination:There are 5 zeros in the matrix which          is more than half of the matrix size.

Question

Find if the matrix is a sparse matrixInput:  1 0 3             0 0 4             6 0 0Output: YesExplaination:There are 5 zeros in the matrix which          is more than half of the matrix size.

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Solution 1

Sure, here is the step by step explanation:

  1. A sparse matrix is a matrix in which most of the elements are zero. By contrast, if most of the elements are nonzero, then the matrix is considered dense.

  2. The given matrix is: 1 0 3 0 0 4 6 0 0

  3. Count the number of zero and non-zero elements in the matrix. In this case, there are 5 zeros and 4 non-zeros.

  4. Compare the number of zeros with the total number of elements in the matrix. If the number of zeros is more than half of the total elements, then the matrix is sparse.

  5. The total number of elements in the matrix is 9 (3 rows * 3 columns). The number of zeros (5) is more than half of the total elements (9).

  6. Therefore, the given matrix is a sparse matrix. The output is "Yes".

This problem has been solved

Solution 2

To determine if a matrix is sparse, we need to check if more than half of its elements are zero.

Step 1: Identify the size of the matrix. In this case, the matrix is a 3x3 matrix, so it has 9 elements in total.

Step 2: Count the number of zero elements in the matrix. In this case, there are 5 zero elements.

Step 3: Compare the number of zero elements to half the total number of elements. If the number of zero elements is greater than half the total number of elements, then the matrix is sparse.

In this case, 5 (the number of zero elements) is greater than 4.5 (half the total number of elements), so the matrix is sparse. Therefore, the output is "Yes".

This problem has been solved

Solution 3

To determine if a matrix is sparse, we need to check if more than half of its elements are zero.

Step 1: Identify the size of the matrix. The size of a matrix is determined by the number of rows multiplied by the number of columns. In this case, the matrix is 3x3, so it has 9 elements.

Step 2: Count the number of zero elements in the matrix. In this case, there are 5 zero elements.

Step 3: Compare the number of zero elements to half the size of the matrix. If the number of zero elements is greater than half the size of the matrix, then the matrix is sparse. In this case, 5 is more than half of 9, so the matrix is sparse.

Therefore, the output is "Yes", the matrix is sparse.

This problem has been solved

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