Which pair of numbers is relatively prime? 10 AND 70

Answer:

a matrix with 1's in the main diagonal and zeros everywhere. The identity matrix of order 2×2 is: [1 0 0 1].

Final answer:

The 2x2 identity matrix is a square matrix with 1s on the main diagonal and 0s elsewhere. It serves as the multiplicative identity in matrix multiplication, leaving the original matrix unchanged when multiplied.

Explanation:

In mathematics, the 2x2 identity matrix, denoted by the symbol I or Id, is a square matrix containing elements that make it act as the multiplicative identity in matrix multiplication. Specifically, a 2x2 identity matrix is written as:

I = [1, 0; 0, 1]

Here, the numbers 1 are positioned on the main diagonal from the top-left to bottom-right (also termed as principal diagonal). The other elements, outside the main diagonal, are 0. This particular configuration results in special properties such as, when any matrix is multiplied by the identity matrix, the original matrix is unchanged. So, if we have a 2x2 matrix A, then multiplying by the identity gives AI = IA = A.

Learn more about 2x2 Identity Matrix here:

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Given:

The length of a rectangle is 5 centimeters less than 2 times the width.

To find:

The polynomial expression that represents the area of the rectangle, then simplify the expression.

Solution:

Let be the width of the rectangle.

The length of a rectangle is 5 centimeters less than 2 times the width.

2 times the width =

5 centimeters less than 2 times the width =

Length of the rectangle =

We know that, the area of a rectangle is:

Therefore, the required polynomial expression is and its simplified form is .