Question

Find all values of $x$ that satisfy the determinant equation $\left|\begin{array}{cc}{2 x} & {1} \\ {x} & {x}\end{array}\right|=3$ (A) $-1$ (B) $-1$ or 1.5 (C) 1.5 (D) $-1.5$ (E) $-1.5$ or 1

Name: Problem 15, Chapter :
Uploaded: 2019-08-28T01:47:40-08:00
Duration: 2 min 16 s
Channel: Dilip Paruchuri
Description: Find all values of x that satisfy the determinant equation | 2 x 1 x x |=3 (A) -1 (B) -1 or 1.5 (C) 1.5 (D) -1.5 (E) -1.5 or 1

   Find all values of $x$ that satisfy the determinant equation $\left|\begin{array}{cc}{2 x} & {1} \\ {x} & {x}\end{array}\right|=3$
(A) $-1$
(B) $-1$ or 1.5
(C) 1.5
(D) $-1.5$
(E) $-1.5$ or 1

Instant Answer

Solved by Expert Dilip Paruchuri

08/28/2019

Step 1

The determinant of a 2x2 matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ is given by $ad - bc$. So, the determinant of the given matrix $\begin{pmatrix} 2x & 1 \\ x & x \end{pmatrix}$ is $(2x \cdot x) - (1 \cdot x) = 2x^2 - x$. Show more…

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Find all values of $x$ that satisfy the determinant equation $\left|\begin{array}{cc}{2 x} & {1} \\ {x} & {x}\end{array}\right|=3$ (A) $-1$ (B) $-1$ or 1.5 (C) 1.5 (D) $-1.5$ (E) $-1.5$ or 1

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Key Concepts

Solving Algebraic Equations

Many problems involving determinants set the determinant equal to a specified number, which results in an algebraic equation. Solving this equation involves algebraic manipulation such as simplifying expressions and isolating the variable, thereby finding the value(s) that satisfy the given condition.

Determinant

A determinant is a scalar attribute computed from a square matrix, reflecting properties like invertibility and area scaling factor in transformations. It plays a vital role in linear algebra, enabling solutions to systems of linear equations and providing insights into the matrix’s behavior.

2x2 Matrix Determinant Formula

For a 2x2 matrix, the determinant is calculated using the formula ad - bc, where a, b, c, and d are the elements of the matrix. This simple formula is particularly useful in problems involving 2x2 matrices, as it directly provides the scalar value that characterizes the matrix.

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