Find the Inverse of the Matrix If It Exists $$\left[ \begin{array} { l l } 5 & 2 \\4 & 9\end{array} \right]$$

question 20

Multiple Choice

Find the inverse of the matrix if it exists. $$\left[ \begin{array} { l l } 5 & 2 \\4 & 9\end{array} \right]$$

• A) \[9 \left[ \begin{array} { l l }
• 5 & 4 \\
• 2 & 1
• \end{array} \right]\]
• B) \[\frac { 1 } { 5 } \left[ \begin{array} { c c }
• 9 & 4 \\
• - 2 & 37
• \end{array} \right]\]
• C) \[\frac { 1 } { 37 } \left[ \begin{array} { c c }
• 9 & - 2 \\
• - 4 & 5
• \end{array} \right]\]
• D) \[\frac { 1 } { 37 } \left[ \begin{array} { c c }
• 63 & - 14 \\
• - 28 & 35
• \end{array} \right]\]
• E) Does not exist

---

Definitions:

Division

Division is a fundamental arithmetic operation that divides a number (the dividend) by another (the divisor) to find a quotient, possibly with a remainder.

Division

A mathematical operation symbolized by ÷ or /, indicating the splitting of a quantity into equal parts or the process of finding how many times one number is contained into another.

Simplify

The process of altering an expression or equation to make it easier to work with, often by combining like terms or using mathematical properties.

Synthetic Division

A streamlined method for dividing polynomials, focusing on the coefficients and omits variables and exponents for efficiency.