Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![**Title: Using Diagonals to Find the Determinant**
**Instructions:** Use diagonals to find the determinant. *(Note: Always use ++--)*
**Matrix:**
\[
\text{det} \begin{bmatrix}
-1 & 3 & -3 \\
4 & -2 & -1 \\
0 & -5 & 2
\end{bmatrix}
\]
**Explanation:**
To find the determinant of a 3x3 matrix using diagonals, follow these steps:
1. **Draw the Matrix:**
- Copy the first two columns of the matrix to the right side of the matrix.
2. **Calculate the Positive Diagonal Products:**
- Multiply the diagonals from the top left to the bottom right.
- For the given matrix, calculate:
- \((-1) \times (-2) \times 2\)
- \(3 \times (-1) \times 0\)
- \((-3) \times 4 \times (-5)\)
3. **Calculate the Negative Diagonal Products:**
- Multiply the diagonals from the bottom left to the top right.
- For the given matrix, calculate:
- \(0 \times (-2) \times (-3)\)
- \((-5) \times (-1) \times (-1)\)
- \(2 \times 4 \times 3\)
4. **Subtract the sums of these products:**
- Add the results of the positive diagonals.
- Add the results of the negative diagonals.
- Subtract the sum of the negative products from the sum of the positive products.
**Visual Aids:**
- Consider using colors to differentiate between the positive and negative diagonals for clarity.
- Use interactive tools where students can draw and practice determining the diagonals themselves.
**Note:** Ensure students are reminded to follow the correct sequence of multiplication and subtraction as described. The use of colors in the matrix image helps to identify each diagonal involved in calculation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbab5ee7e-727a-4c4c-8a8b-4a451826ec00%2F14ae6106-6431-46b3-8925-3103607866aa%2F9ug1xyh_processed.jpeg&w=3840&q=75)
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