In this video we are going to discuss matrices and focus on multiplying a matrix by a scalar. When I say a scalar what I mean is a real number. We're going to take a matrix and we're going to multiply each entry of the matrix by a real number k to get the resulting matrix. Let's take a look at two examples. Here, we have example four, and in example four we are going to begin by finding negative one-half times matrix C. When we begin, we want to distribute the negative one-half to each entry of our matrix C. We will start by writing our matrix with the negative one-half multiplied to each entry of matrix C, making sure to keep all of the positive and negative symbols. Our second row we do the same thing so I have negative one half times five, negative one half times seven, and last, negative one-half times negative one our final step will be that we will actually do the multiplication in each entry so you have negative three halves, negative three, positive nine halves, negative five halves, negative seven halves, and positive one-half as the result of taking and multiplying negative one-half to matrix C. In example for part b we are going to look at taking and finding the operation of negative six B plus seven A and finding out what our resulting matrix is. First, if you recall from our discussions on addition matrix B and matrix A must be the same size matrices. We see that both are two by two matrices so we can move on to distributing the scalar to each of our corresponding matrices. We will start with taking and multiplying negative six to each entry of matrix B which gives us negative six times one, negative six times negative 11, then negative six times three y and negative six times positive 18. To that, we will add what happens when we multiply seven to each entry of matrix A. So you have seven times negative two, seven times four x, seven times y and then seven times eight. Our next step is to simplify each entry in each of our matrices before we add. So I will have negative six, 66, negative 18y and negative 108. To that I want to add negative 14, 28 x, seven y, and 56. Since we've already discussed adding matrices, I'm simply going to add corresponding entries and write my final answer. So negative six B plus seven A has a resulting matrix of negative 20, then 28 x plus 66, a negative 11y, and negative 52 as my entries. and again if you prefer you can always put parentheses around your entry that had the sum but this is your resulting matrix when you have negative six B plus seven A.