Tutor profile: Hannah W.
Subject: Linear Algebra
Can a 5x3 matrix and a 5x3 matrix be multiplied together?
The answer is no. A matrix is described as m x n ("m by n"), where m refers to the number of rows and n refers to the number of columns. Two matrices can only be multiplied together when the number of rows of the first matrix is equal to the number of columns in the second matrix. i.e., a 3x2 matrix can be multiplied by a 2x4 matrix.
What is the circumference of a circle with diameter 12 cm?
We can solve this using the formula that relates circumference and diameter, Circumference = π * diameter, aka C = π * d. We know C = 12 cm, so we plug that into the formula. C = π * 12. We can leave the answer as 12π, or use 3.14 (the shorthand for Pi) to find the number. C = 37.68 cm or 12π cm.
Subject: Basic Math
3 + (11-5) x 2 = ?
This is a question demonstrating the use of the order of operations, PEMDAS. The solutions is to do what's in the parenthesis first: 11-5 = 6, which makes the equation look like 3 + (6) x 2 = ? Using the order of operations, 6 x 2 = 12 is completed next. The equation now looks like this: 3 + 12 = ? Finally, the equation can be solved to be 15.
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