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Here we will solve different types of Problems on Matrix Multiplication. 1. If A = \(\begin{bmatrix} 1 & -2 & 1\\ 2 & 1 & 3 \end{bmatrix}\) and B = \(\begin{bmatrix} 2 & 1\\ 3 & 2\\ 1 & 1 \end{bmatrix}\), write down the matrix AB. Would it be possible to find the product of BA? If so, compute it, and if not, give reasons. Solutions:
To multiply a matrix by a single number is easy: These are the calculations: We call the number ("2" in this case) a scalar, so this is called "scalar multiplication". Multiplying a Matrix by Another Matrix. But to multiply a matrix by another matrix we need to do the "dot product" of rows and columns ... what does that mean?
On this post you will see how to calculate a matrix multiplication. We explain the procedure of multiplying matrices step by step through an example, and then you will find solved exercises so that you can also practice. Finally, you will learn when two matrices cannot be multiplied and all the properties of this matrix operation.
6 paź 2021 · Example \(\PageIndex{3}\): Multiplying the Matrix by a Scalar. Multiply matrix \(A\) by the scalar \(3\). \[A=\begin{bmatrix}8&1\\5&4\end{bmatrix} \nonumber\] Solution. Multiply each entry in \(A\) by the scalar \(3\).
Multiplication of Matrices. Important: We can only multiply matrices if the number of columns in the first matrix is the same as the number of rows in the second matrix. Example 1. a) Multiplying a 2 × 3 matrix by a 3 × 4 matrix is possible and it gives a 2 × 4 matrix as the answer.
On this page you can see many examples of matrix multiplication. You can re-load this page as many times as you like and get a new set of numbers and matrices each time. You can also choose different size matrices (at the bottom of the page).
These worksheets explain how to multiply matrices of equal or different sizes together and how to multiply a matrix by a number. The matrices may be in 1x2, 2x2, 2x3, or 3x3 configurations.
