1 16. x' = -2 -2 -3 3 4
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.
![The image displays a matrix equation used in linear algebra. Here's the transcription suitable for an educational website:
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**Matrix Equation:**
Consider the transformation represented by the following matrix equation:
**16.** \(\mathbf{x'} = \begin{bmatrix} 1 & 0 & 0 \\ -2 & -2 & -3 \\ 2 & 3 & 4 \end{bmatrix} \mathbf{x}\)
**Explanation:**
This is a matrix-vector multiplication where \(\mathbf{x'}\) is the resultant vector obtained by multiplying the given 3x3 matrix with the vector \(\mathbf{x}\). Each element of \(\mathbf{x'}\) is computed as a linear combination of the elements of \(\mathbf{x}\) with the corresponding coefficients from each row of the matrix.
- The first row \([1, 0, 0]\) suggests that the first element of \(\mathbf{x'}\) will be influenced only by the first element of \(\mathbf{x}\).
- The second row \([-2, -2, -3]\) indicates a linear combination involving all elements of \(\mathbf{x}\) with respective coefficients.
- The third row \([2, 3, 4]\) involves a different linear combination of all elements in \(\mathbf{x}\).
This matrix can be used in various applications such as transformations in space, solving systems of equations, and modeling dynamic systems.
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