Solve for x in the following matrix equation.
[5x-8 1] = [2 1]
[3 4m-1] [3 7m+6]
How do you do this? I hardly know anything about this... The packet I got that was supposed to help me understand matrices and stuff just made me more confused.
each element must be identical in the two matrices (you already have 1=1 and 3=3), so you just have to solve
5x-8 = 2
4m-1 = 7m+6
then use those values to fill in the unknown elements.
since the two matrices are equal, corresponding elements of the matrices are also equal.
so : 5x -8 = 2
5x - 8 + 8 = 2 + 8
5x = 10
x = 2
To solve the matrix equation, we need to equate the corresponding elements of the two matrices.
For the first row and first column, we have:
5x - 8 = 2
Simplifying this equation gives us:
5x = 10
Dividing both sides by 5, we get:
x = 2
Now, let's move on to the second row and second column. We have:
4m - 1 = 7m + 6
To solve for m, we need to isolate it on one side of the equation. Let's subtract 4m from both sides and add 1 to both sides:
-1 - 1 = 7m - 4m + 6
-2 = 3m + 6
Next, let's subtract 6 from both sides:
-2 - 6 = 3m
-8 = 3m
Finally, divide both sides by 3 to solve for m:
m = -8/3
So, the solution to the matrix equation is x = 2 and m = -8/3.
To solve for x in a matrix equation, you need to perform matrix operations. Let's break it down step by step:
Step 1: Write the equation in matrix form:
[5x-8 1] = [2 1]
[3 4m-1] [3 7m+6]
Step 2: Equate the corresponding elements in each matrix.
5x - 8 = 2 -> (equation 1)
3 = 3
3 = 7m + 6 -> (equation 2)
4m - 1 = 1
Step 3: Solve the simultaneous equations.
From equation 2, we can rewrite it as:
3 = 7m + 6
Subtract 6 from both sides:
-3 = 7m
Divide both sides by 7:
m = -3/7
Now, let's substitute this value for m back into equation 1 and solve for x.
5x - 8 = 2
Add 8 to both sides:
5x = 10
Divide both sides by 5:
x = 2
Therefore, the solution to the matrix equation is x = 2, m = -3/7.
Understanding matrices and solving matrix equations can be a bit confusing at first, but with practice and familiarity, it becomes easier. Make sure to review the basic matrix operations, such as addition, subtraction, and multiplication, as they are essential in solving matrix equations. Additionally, understanding simultaneous equations and solving them will also be helpful. Don't hesitate to ask if you have any further questions!