Is it me or does this problem not make sense? (you can't solve it)
5. Solve for x in the following system:
6x + 6y = -2
y = -x
I also need help in these:
38. We can take the product AB only if the number of columns of A equals the number of rows of B. -True?
40. The graph of the following system yields perpendicular lines:
x + 2y = -10
-4y = 2x + 20
True or False?
42. If we multiply a 2 x 2 matrix with a 2 x 1 matrix, the product is a 2 x 1 matrix.
-False?
Thanks
-MC
There is no solution, the lines are parallel.
38. true
40. put each in slope intercept form:
y=-x/2 -5
y=-x/2 -5
false, it is the same line.
Wait, so 42 IS false?
-MC
Problem 5:
To solve the system of equations:
6x + 6y = -2 (1)
y = -x (2)
We can substitute equation (2) into equation (1) to eliminate y and solve for x:
6x + 6(-x) = -2
6x - 6x = -2
0 = -2
As you can see, this equation leads to an inconsistency since 0 cannot equal -2. Therefore, this system of equations has no solution.
Problem 38:
The statement "We can take the product AB only if the number of columns of A equals the number of rows of B" is TRUE.
The product of two matrices is only defined if the number of columns in the first matrix (A) is equal to the number of rows in the second matrix (B). This rule ensures that the dimensions of the resulting matrix are compatible.
Problem 40:
To determine if the lines represented by the system of equations are perpendicular, we need to check the slopes of the lines.
The given system of equations:
x + 2y = -10 (1)
-4y = 2x + 20 (2)
We can rewrite equation (1) in slope-intercept form: y = -0.5x - 5
And equation (2) can be rewritten as: y = -0.5x - 5
Since both equations have the same slope (-0.5), the lines are parallel, not perpendicular. Therefore, the statement "The graph of the following system yields perpendicular lines" is FALSE.
Problem 42:
The statement "If we multiply a 2 x 2 matrix with a 2 x 1 matrix, the product is a 2 x 1 matrix" is FALSE.
When multiplying matrices, the number of columns in the first matrix (2) must be equal to the number of rows in the second matrix (2). In this case, a 2 x 2 matrix multiplied by a 2 x 1 matrix would result in a 2 x 2 matrix, not a 2 x 1 matrix.
I hope this helps clarify your questions. Let me know if there's anything else I can explain!