What will be the result of executing C - 8 if C is given by C = [15 4 12; -2 17 11]?

Understand the Problem

The question is asking for the result of performing matrix subtraction, specifically subtracting the scalar value 8 from each element of the matrix C. We will perform the operation by subtracting 8 from each element of the matrix defined as C = [15 4 12; -2 17 11].

Answer

$$ C' = \begin{bmatrix} 7 & -4 & 4 \\ -10 & 9 & 3 \end{bmatrix} $$

Steps to Solve

Define the matrix C

The matrix defined in the problem is

$$ C = \begin{bmatrix} 15 & 4 & 12 \ -2 & 17 & 11 \end{bmatrix} $$

Subtract the scalar value from each element

We need to subtract the scalar value 8 from each element in the matrix.

For each element ( c_{ij} ) of the matrix C, the operation will look like this:

$$ C' = C - 8 = \begin{bmatrix} 15 - 8 & 4 - 8 & 12 - 8 \ -2 - 8 & 17 - 8 & 11 - 8 \end{bmatrix} $$

Calculate the new values

Now, we do the calculations for each element:

First row:
- ( 15 - 8 = 7 )
- ( 4 - 8 = -4 )
- ( 12 - 8 = 4 )
Second row:
- ( -2 - 8 = -10 )
- ( 17 - 8 = 9 )
- ( 11 - 8 = 3 )

Assemble the new matrix

Putting all the calculated values into a new matrix, we have the result:

$$ C' = \begin{bmatrix} 7 & -4 & 4 \ -10 & 9 & 3 \end{bmatrix} $$

The resulting matrix after subtracting 8 from each element of matrix C is

$$ C' = \begin{bmatrix} 7 & -4 & 4 \ -10 & 9 & 3 \end{bmatrix} $$

More Information

Matrix subtraction involves reducing each element of the matrix by the same scalar amount. This is a fundamental concept in linear algebra often used in various fields such as physics, computer science, and engineering.

Tips

Forgetting to subtract from each individual element: It’s important to apply the subtraction operation to every element in the matrix.
Not maintaining the structure of the matrix: Ensure the resulting values are organized in the same format as the original matrix.

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