If A is a 3x3 matrix and B is a 3x3 matrix, what is the maximum number of non-ze
Practice Questions
Q1
If A is a 3x3 matrix and B is a 3x3 matrix, what is the maximum number of non-zero elements in A + B? (2021)
9
6
3
0
Questions & Step-by-Step Solutions
If A is a 3x3 matrix and B is a 3x3 matrix, what is the maximum number of non-zero elements in A + B? (2021)
Step 1: Understand that A and B are both 3x3 matrices. This means each matrix has 3 rows and 3 columns.
Step 2: Calculate the total number of elements in one 3x3 matrix. Since there are 3 rows and 3 columns, the total is 3 * 3 = 9 elements.
Step 3: Recognize that each element in matrix A can be either zero or non-zero, and the same applies to matrix B.
Step 4: To find the maximum number of non-zero elements in the sum A + B, we need to consider the best-case scenario where all elements in both matrices are non-zero.
Step 5: If all 9 elements in matrix A are non-zero and all 9 elements in matrix B are also non-zero, then when we add A and B together, each of the 9 elements in A + B will also be non-zero.
Step 6: Therefore, the maximum number of non-zero elements in A + B is 9.
