oltain The feterminant f The matria 3. 2-3 /- -3 5
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
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![Title: Finding the Determinant of a Matrix
**Problem Statement:**
Obtain the determinant of the matrix
\[ \begin{pmatrix}
2 & 0 & 1 \\
3 & 2 & -3 \\
-1 & -3 & 5
\end{pmatrix} \]
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In this problem, you are required to find the determinant of the given 3x3 matrix. The matrix is composed of three rows and three columns:
\[ \begin{pmatrix}
2 & 0 & 1 \\
3 & 2 & -3 \\
-1 & -3 & 5
\end{pmatrix} \]
This is a key concept in Linear Algebra and is crucial for understanding various properties of matrices, such as whether a system of linear equations has a unique solution, among other applications.
**Procedure:**
To find the determinant of a 3x3 matrix, you can use the rule of Sarrus or cofactor expansion. For this specific matrix, the determinant (denoted as |A|) is calculated as follows:
\[ \text{det}(A) = a(ei - fh) - b(di - fg) + c(dh - eg) \]
where the matrix is:
\[ \begin{pmatrix}
a & b & c \\
d & e & f \\
g & h & i
\end{pmatrix} \]
For our given matrix:
\[ a = 2, \; b = 0, \; c = 1 \]
\[ d = 3, \; e = 2, \; f = -3 \]
\[ g = -1, \; h = -3, \; i = 5 \]
Plug these values into the determinant formula to find the result.
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By following these steps, students should be able to successfully determine the determinant of the given matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faaa612e4-bb6a-4a7c-9bcb-a4980796bdd1%2Fb17f71df-bb69-4ace-84f0-18cddbeed5a1%2Fs5i9185_reoriented.jpeg&w=3840&q=75)
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