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Two matrices A and B are multiplied to get AB, if
- a)No of rows of A is equal to no of columns of B
- b)no of columns of A is equal to rows of B
- c)both are rectangular
- d)both have same order
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two matrices A and B are multiplied to get AB, ifa)No of rows of A is ...
Two matrices A and B are multiplied to get AB if the number of columns of matrix A is equals to the number of rows of matrix B.
The product of two matrices A and B is defined if the number of columns of matrix A is equal to number of rows of matrix B. Let A = [aij] be an mxn matrix & B = [bjk] be an nxp matrix. Then the product of A and B is order of mxp.
Hence, the answer is no of columns of A is equal to rows of B.
The product of two matrices A and B is defined if the number of columns of matrix A is equal to number of rows of matrix B. Let A = [aij] be an mxn matrix & B = [bjk] be an nxp matrix. Then the product of A and B is order of mxp.
Hence, the answer is no of columns of A is equal to rows of B.
Most Upvoted Answer
Two matrices A and B are multiplied to get AB, ifa)No of rows of A is ...
Explanation:
When we multiply two matrices, the order of the matrices matters. Matrix A and B can be multiplied only if the number of columns of matrix A is equal to the number of rows of matrix B. Let us understand this concept in detail:
Matrix Multiplication:
Matrix multiplication is the operation that takes two matrices as input and produces a third matrix as output. We can multiply two matrices only when the number of columns of the first matrix is equal to the number of rows of the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.
Order of Matrices:
The order of a matrix is the number of rows and columns it has. If a matrix has m rows and n columns, we write its order as m x n. For example, a matrix with 2 rows and 3 columns has an order of 2 x 3.
Multiplying Matrices:
When we multiply two matrices A and B, the resulting matrix C has the same number of rows as A and the same number of columns as B. The element cij in the resulting matrix C is obtained by multiplying the elements in the ith row of matrix A with the elements in the jth column of matrix B and adding the products.
Answer:
In this question, we are given two matrices A and B, and we are asked to determine the conditions under which they can be multiplied. The correct answer is option 'B', which states that the number of columns of matrix A is equal to the number of rows of matrix B. This condition is necessary for matrix multiplication to be possible. If the number of columns of matrix A is not equal to the number of rows of matrix B, then we cannot multiply the matrices.
When we multiply two matrices, the order of the matrices matters. Matrix A and B can be multiplied only if the number of columns of matrix A is equal to the number of rows of matrix B. Let us understand this concept in detail:
Matrix Multiplication:
Matrix multiplication is the operation that takes two matrices as input and produces a third matrix as output. We can multiply two matrices only when the number of columns of the first matrix is equal to the number of rows of the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.
Order of Matrices:
The order of a matrix is the number of rows and columns it has. If a matrix has m rows and n columns, we write its order as m x n. For example, a matrix with 2 rows and 3 columns has an order of 2 x 3.
Multiplying Matrices:
When we multiply two matrices A and B, the resulting matrix C has the same number of rows as A and the same number of columns as B. The element cij in the resulting matrix C is obtained by multiplying the elements in the ith row of matrix A with the elements in the jth column of matrix B and adding the products.
Answer:
In this question, we are given two matrices A and B, and we are asked to determine the conditions under which they can be multiplied. The correct answer is option 'B', which states that the number of columns of matrix A is equal to the number of rows of matrix B. This condition is necessary for matrix multiplication to be possible. If the number of columns of matrix A is not equal to the number of rows of matrix B, then we cannot multiply the matrices.
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Two matrices A and B are multiplied to get AB, ifa)No of rows of A is equal to no of columns of Bb)no of columns of A is equal to rows of Bc)both are rectangulard)both have same orderCorrect answer is option 'B'. Can you explain this answer?
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