# Tutor profile: Usman J.

## Questions

### Subject: Linear Algebra

For the matrix below, determine the order and state whether it is a square matrix. $$\begin{bmatrix} -6 & 2 & 0\\ 3 & -3 & 4\\ -5 & -11 & 9 \end{bmatrix}$$

Since there are 3 rows and 3 columns the order is: 3 x 3 In order for a matrix to be a square matrix the number of rows must equal to number of columns. Since there are 3 row and 3 columns and number of rows = number of columns, this is a square matrix.

### Subject: Basic Math

What is 8 x 10 ÷ 5 + 6 - (6 ÷ 2) ?

In order to answer this question correctly, we must follow the BEDMAS order of operations. BEDMAS or Brackets, Exponents, Division, Multiplication, Addition, Subtraction is the order in which we must evaluate to solve any given operation. To simplify, we must perform operations in Brackets first, then Exponent operations, then Division operations, etc. So to solve our given question, let's observe which operations are present in the questions and solve them step-by-step. Using BEDMAS, we must evaluate any operations in with the first order of operations which is "B" or Brackets. 8 x 10 ÷ 5 + 6 - (6 ÷ 2) As we can see, the terms within the Brackets (6 ÷ 2) must first be solved first. This gives us 6 ÷ 2 = 3 So, by replacing 6 ÷ 2 with 3, our new equation is: 8 x 10 ÷ 5 + 6 - 3 Now, using BEDMAS again, the second order of operations is "E" or Exponents. Since there aren't any exponents in our equation we skip it and move onto the next order of operation. The next operation is "D" or Division. Analyzing our equation we can see there is a division symbol between 10 and 5. Evaluating 10 ÷ 5 would give us 2. So, by replacing 10 ÷ 5 with 2, our new equation is: 8 x 2 + 6 - 3 Using BEDMAS again, the next order of operation is "M" or Multiplication We can see there is a multiplication term "X" between 8 and 2. Evaluating 8 x 2 gives us 16. So, by replacing 8 x 2 with 16, our new equation is: 16 + 6 - 3 We are left with Addition and Subtraction. Using BEDMAS as a rule of thumb, we can understand that "A" or Addition comes before "S" or Subtraction. So, we must Add before we Subtract. We can see that 16 and 3 are being added. 16 + 3 gives us 19. So, by replacing 16 + 3 with 19, our new equation would be: 19 - 3 We are left with one last operation which is subtraction. This is the last order of operation in BEDMAS. 19 minus 3 gives us 16. Replacing 19 - 3 with 16, our final answer is: = 16 So, 8 x 10 ÷ 5 + 6 - (6 ÷ 2) = 16.

### Subject: Algebra

Evaluate 11x - 7 given that x - 3 = 14

In order to solve 11x - 7 we must first evaluate what x is equal to. Considering x - 3 = 14 we can isolate for x term by moving "3" to the right side to give: x = 14 + 3 x = 17 Now that x term has been solved to equal 17, we can plug in this value for 11x - 7 11x - 7 11(17) - 7 187 - 7 = 180 In conclusion, given that x - 3 = 14, it can be solved that 11x - 7 is equal to 180.

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