In this tutorial, we will learn how to multiply a matrix by a constant in R. Matrix multiplication by a constant, also known as scalar multiplication, involves multiplying each element of the matrix by a constant value.

This is a common operation in linear algebra and is widely used in various applications such as data manipulation, computer graphics, and machine learning.

### Step 1: Create a Matrix in R

First, we will create a matrix in R using the **matrix()** function. This function takes in a vector of values, and we can specify the number of rows and columns for the resulting matrix.

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mat <- matrix(c(1, 2, 3, 4, 5, 6), nrow = 2, ncol = 3) print(mat) |

[,1] [,2] [,3] [1,] 1 3 5 [2,] 2 4 6

We have created a 2×3 matrix named **mat** where the numbers 1 through 6 are arranged in two rows and three columns.

### Step 2: Multiply the Matrix by a Constant

Now that we have our matrix, let’s multiply it by a constant. In R, you simply multiply the matrix by the constant using the ***** operator. For example, let’s multiply the matrix by the constant 3.

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constant <- 3 result <- mat * constant print(result) |

[,1] [,2] [,3] [1,] 3 9 15 [2,] 6 12 18

As you can see, each element of the matrix has been multiplied by the constant value 3.

### Step 3: Verify the Result

To verify that the result is correct, you can think of the constant as a 1×1 matrix with a value equal to the constant. Then, perform the element-wise multiplication of the matrices.

We can achieve this by defining the constant as a 1×1 matrix using the **matrix()** function and performing element-wise multiplication using the sweep() function.

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constant_matrix <- matrix(constant, nrow = 1, ncol = 1) output <- sweep(mat, 1, constant_matrix, "*") print(output) |

[,1] [,2] [,3] [1,] 3 9 15 [2,] 6 12 18

The output is the same as before, which confirms that multiplying a matrix by a constant works as expected.

## Full code:

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# Create a matrix mat <- matrix(c(1, 2, 3, 4, 5, 6), nrow = 2, ncol = 3) print(mat) # Multiply the matrix by a constant constant <- 3 result <- mat * constant print(result) # Verify the result using sweep function constant_matrix <- matrix(constant, nrow = 1, ncol = 1) output <- sweep(mat, 1, constant_matrix, "*") print(output) |

## Conclusion

In this tutorial, we learned how to multiply a matrix by a constant in R. We created a matrix using the matrix() function, multiplied the matrix by a constant using the * operator, and verified the result using the sweep() function.

Scalar multiplication is fundamental in linear algebra, and its implementation in R is straightforward and intuitive.