In Exercises 1 - 4,
a. Give the order of each matrix,
b. If A = [...

Question

In Exercises 1 - 4, a. Give the order of each matrix, b. If A = [a_ij], identify a_32 and a_23, or explain why identification is not possible, 4 - 7 5 - 6 8 - 1 (please enclose the values above in a matrix symbol)

Matrix showing values: [4 -7 5; -6 8 -1] for college algebra exercise.

Accepted Answer

hey everyone here we are asked to find the matrix order. As well as find values for a sub 13 and a sub 31. So we can start by just rewriting our given matrix. So it's first row has the values negative 52 and three. And it's second row has the values one, negative three and seven. And now to find the matrix order, we have to recall that the order of a matrix is denoted as M by N. Where M is the number of rows and the end is the number of columns. So from here we just have to look at our given matrix and see that it has 12 roads. So our M. Is equal to two and then it has 123 columns. So our N. Is equal to three. And now we can write the order of the matrix which is M by M. So we have a two by three matrix. And now we are also So asked to find a sub 13 and a sub 31 but we are told that capital a is equal to the matrix of lower case. A sub I and J. So here I is the row and J is the column. So with this information we can identify the row and column by looking at the subscript of both of our terms here. So starting with a sub 13, 1 is the first value. So we see that eye is one and then J. The second value here is three. So now we look at our matrix and we go to row one And then we go to column three and we land on the value here, which is just three. So we see that a sub is equal to three. And now we can repeat this with our second Value we're trying to find which is a sub 31, so I is equal to three and J is equal to one. So we would go to row three. But as you can see we do not have a third row. So we know that a sub 31 does not exist. So now we have found all of the information we were trying to find. So we're left with answer choice D. Where we have a two by three matrix A sub 13 is equal to three and a sub 31 does not exist, since there are only two rows. Thanks for watching, I hope you found this video helpful and I'll see you again next time.

In Exercises 1 - 4, a. Give the order of each matrix, b. If A = [a_ij], identify a_32 and a_23, or explain why identification is not possible, 4 - 7 5 - 6 8 - 1 (please enclose the values above in a matrix symbol)

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