1) What is the dimension of AB given A is a 5 × 6 matrix and B is a 6 × 3 matrix?
for the second questions, it is a fill in a blank question.
2) A point of intersection of the graphs of the equations of a system is a ? of the system.
the ? is where one of these answers come in:
a) break-even point
b) y-intercept
c) solution
d) x-intercept
1) 5 x 3
2) Solution
thanks Unknown
1) To determine the dimension of the matrix AB, we need to consider how matrix multiplication works. When multiplying a matrix A with dimensions m x n by another matrix B with dimensions n x p, the resulting matrix AB will have dimensions m x p.
In this case, A is a 5 x 6 matrix and B is a 6 x 3 matrix. Since the number of columns in A matches the number of rows in B (6), the resulting matrix AB will have dimensions 5 x 3. Therefore, the dimension of AB is a 5 x 3 matrix.
2) In the given list of options, the correct answer to complete the sentence for the second question is "c) solution."
When solving a system of equations, a point of intersection represents a solution to the system. This is because the coordinates of the point satisfy all the equations simultaneously, indicating that it is a valid solution for the system.