Final answer:
Multiplying a 2x2 matrix by a 2x3 matrix results in a 2x3 matrix, which is achieved by row-by-column multiplication summing the products of the corresponding elements. In linear algebra, matrices play an important role in dealing with different concepts. A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns in mathematics.
Step-by-step explanation:
When you multiply a 2x2 matrix by a 2x3 matrix, you will end up with a matrix that has the same number of rows as the first matrix and the same number of columns as the second matrix. Therefore, the product of a 2x2 matrix and a 2x3 matrix is a 2x3 matrix.
The multiplication process involves taking the rows from the first matrix and the columns from the second matrix, and multiplying the corresponding elements and then summing them up to get each element of the resulting matrix. This is a fundamental concept in matrix algebra and is often used in various applications in mathematics and engineering.
In linear algebra, matrices play an important role in dealing with different concepts. A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns in mathematics. We can perform various operations on matrices such as addition, subtraction, multiplication and so on.
We know that a matrix is an array of numbers. It consists of rows and columns. If you multiply a matrix by a scalar value, then it is known as scalar multiplication. Another case is that it is possible to multiply a matrix by another matrix. Let’s have a look at the example given below for the same.
We may define multiplication of a matrix by a scalar mathematically as:
If A = [aij]m × n is a matrix and k is a scalar, then kA is another matrix obtained by multiplying each element of A by the scalar k.