Adjacency and Incidence Matrices are used to store vertices and edges of a graph. It is an advantage to plot graphs easily using matrices. But Time complexity of a matrix is O(n2) and sometimes the internal organization becomes tedious. They are all disadvantages of matrices.
Workspace
NA
SHSTTON
154
Solv. Corr.
43
Solv. In. Corr.
197
Attempted
0 M:0 S
Avg. Time
2 / 13
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If column-major order is used, how is the following matrix stored in memory?
It starts with the first element and continues in the same column until the end of column is reached and then proceeds with the next column. Fortran follows column-major order.
Workspace
NA
SHSTTON
31
Solv. Corr.
47
Solv. In. Corr.
78
Attempted
0 M:0 S
Avg. Time
3 / 13
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Which of the following is not the method to represent Sparse Matrix?
Heap is not used to represent Sparse Matrix while in Dictionary, rows and column numbers are used as Keys and values as Matrix entries, Linked List is used with each node of Four fields (Row, Column, Value, Next Node) (2D array is used to represent the Sparse Matrix with three fields (Row, Column, Value).
Workspace
NA
SHSTTON
47
Solv. Corr.
19
Solv. In. Corr.
66
Attempted
0 M:0 S
Avg. Time
4 / 13
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Is O(n) the Worst case Time Complexity for addition of two Sparse Matrix?
In Addition, the matrix is traversed linearly, hence it has the time complexity of O(n) where n is the number of non-zero elements in the largest matrix amongst two.
Numbers uses arrays(1-D) for sorting not matrices(2-D arrays). Solving linear equations is a separate field in Mathematics involving matrices, Image processing stores the pixels in the form of matrices, and the graphs are represented with the help of matrices to indicate the nodes and edges.
Workspace
NA
SHSTTON
9
Solv. Corr.
57
Solv. In. Corr.
66
Attempted
0 M:0 S
Avg. Time
6 / 13
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Which one of the following is a Special Sparse Matrix?
A band matrix is a sparse matrix whose non zero elements are bounded to a diagonal band, comprising the main diagonal and zero or more diagonals on either side.
Workspace
NA
SHSTTON
28
Solv. Corr.
39
Solv. In. Corr.
67
Attempted
0 M:0 S
Avg. Time
7 / 13
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Matrix A when multiplied with Matrix C gives the Identity matrix I, what is C?
Sparse Matrix is a matrix in which most of the elements are Zero. Identity Matrix is a matrix in which all principle diagonal elements are 1 and rest of the elements are Zero. Unit Matrix is also called Identity Matrix. Zero Matrix is a matrix in which all the elements are Zero.
Workspace
NA
SHSTTON
7
Solv. Corr.
45
Solv. In. Corr.
52
Attempted
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Avg. Time
9 / 13
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What is the relation between Sparsity and Density of a matrix?
Sparsity of a matrix is equal to 1 minus Density of the matrix. The Sparsity of matrix is defined as the total number of Zero Valued elements divided total number of elements.
Workspace
NA
SHSTTON
22
Solv. Corr.
23
Solv. In. Corr.
45
Attempted
0 M:22 S
Avg. Time
10 / 13
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Select the code snippet which performs matrix multiplication.(a and b are the two given matrices, resultant marix is c)
I. for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
for (int k = 0; k < n; k++)
{
c[i][j] = c[i][j] + a[i][j] + b[k][j];
}
}
}
II. for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
for (int k = 0; k < n; k++)
{
c[i][j] = c[i][j] * a[i][k] * b[k][j];
}
}
}
III. for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
for (int k = 0; k < n; k++)
{
c[i][j] = c[i][j] + a[i][k] + b[k][j];
}
}
}
IV. for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
for (int k = 0; k < n; k++)
{
c[i][j] = c[i][j] + a[i][k] * b[k][j];
}
}
}
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