Question

Matrix a is a 6 × 5 matrix. which order of matrix can be multiplied by matrix a to create matrix ab?

Answer 1

Order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

What is a matrix?

• A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics.
• For instance, consider a matrix with two rows and three columns.

To find the order of matrix:

• We must first check the dimension of two matrices, say matrix A by matrix B, before we may multiply them.
• Multiplication is achievable if the number of columns in the first matrix, A, equals the number of rows in the second matrix.
• Dimension is assigned to the provided matrix: 6 × 5
• This means the given matrix contains six rows and five columns.
• As a result, the second matrix MUST have 5 rows in order for multiplication to be POSSIBLE.
• The only matrix with 5 rows among the above alternatives is the matrix with dimension (B) 5 × 6.

To prove:

• In other words, the inner products of the dimensions should be equal.
• That is; (a × b)(b × a) is possible but (a ×b)(c × b) is impossible.
• The dimensions of the matrix are given by, row × column.

Therefore, order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.

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