In Exercises 5 - 8, find values for the variables so that the ...

Question

In Exercises 5 - 8, find values for the variables so that the matrices in each exercise are equal. $\begin{bmatrix}x \4\end{bmatrix}=\begin{bmatrix}6 \y\end{bmatrix}$

Accepted Answer

Hey everyone here we are asked to determine the values for the variables that make these two matrices equal. So on the left hand side we have a single column matrix with the values X and nine. And it is equal to the other single column matrix with the values negative seven Y. So first before we can determine the values of X and Y. We must recall that. In order for two matrices, let's say matrix A must be equal to matrix B. If and only if they have the same order. So that means the M by N. For A must be equal to the M by N. For matrix B. Additionally a sub Ij must be equal to B sub I. J. Where I is some number M and J is some number N. And so from here let's deny our left hand side matrix as matrix A. And our right hand side matrix as matrix B. So now again, in order for a to be equal to be their orders must be equal. Well, taking a look at matrix A. Well, matrix A has two rows and it has one column. So it is a two by one, matrix. And matrix B also has two rows and one column. So it is also a two by one matrix. And now we can move on to check the other condition. So to check this second condition here, we can take a look at this variable X. Well X is the at row one and column one. So it is equal to a sub 11. Well, we now know that a sub 11 must be equal to B. Sub 11. And we if we look at matrix B at row one, column one which is B sub 11, we have the value negative seven. So it is equal to negative seven. And now we can clearly see that X must be equal to negative seven. And now we can repeat this concept. Taking a look at why? So why is at B sub 12 or sorry? Sub 21, which must also be equal to a sub 21 at wrote to column one for matrix A. We have the value nine. So now we can clearly see that Y must also be equal to nine. And that leaves us with answer choice B where X is negative seven and y is nine. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

In Exercises 5 - 8, find values for the variables so that the matrices in each exercise are equal. $\begin{bmatrix}x \\4\end{bmatrix}=\begin{bmatrix}6 \\y\end{bmatrix}$

Key Concepts

Matrix Equality

Solving for Variables in Matrices

Basic Algebraic Manipulation

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