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Chapter 4: Q1. (page 185)

Write a matrix whose determinant is zero.

Short Answer

Expert verified

A matrix whose determinant is zero $[\begin{matrix} - 3 & - 6 \\ 2 & 4 \end{matrix}]$ .

Step by step solution

01

- Define the determinant of second-order matrix

The determinant of second order matrix is found by calculating the difference of the product of the two diagonals, that is., $|\begin{matrix} a & b \\ c & d \end{matrix}| = a d - b c$ .

02

- Find the Matrix

Let a matrix whose determinant is zero be $[\begin{matrix} - 3 & - 6 \\ 2 & 4 \end{matrix}]$ . Then,

$|\begin{matrix} - 3 & - 6 \\ 2 & 4 \end{matrix}| = - 3 \times (4) - (- 6) (2)$

03

- Simplify

To further verify simplify by multiplying the values first.

$\begin{matrix} |\begin{matrix} - 3 & - 6 \\ 2 & 4 \end{matrix}| = - 3 \times (4) - (- 6) (2) \\ = - 12 + 12 \\ = 0 \end{matrix}$

Hence, verified. A matrix whose determinant is zero is $[\begin{matrix} - 3 & - 6 \\ 2 & 4 \end{matrix}]$ .

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Most popular questions from this chapter

Solve each equation.

$[\begin{matrix} 3 x - 5 & x + y \\ 12 & 9 z \end{matrix}] = [\begin{matrix} 10 & 8 \\ 12 & 3 x + y \end{matrix}]$

Determine the row and column which 100 occur.

$[\begin{matrix} 1 & 3 & 6 & 10 & 15 & \dots \\ 2 & 5 & 9 & 14 & 20 & \dots \\ 4 & 8 & 13 & 19 & 26 & \dots \\ 7 & 12 & 18 & 25 & 33 & \dots \\ 11 & 17 & 24 & 32 & 41 & \dots \\ 16 & 23 & 31 & 40 & 50 & \dots \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \end{matrix}]$

State the dimensions of each matrix.

11. $[\begin{matrix} 7 \\ 8 \\ 9 \end{matrix}]$

For Exercises 36-39, use the following price list for one-day admissions to the community pool.

37. Find the matrix that represents the additional cost for non-residents.

Solve each system of equations.

\begin{matrix} 3 r - 15 s + 4 t = - 57 \\ 9 r + 45 s - t = 26 \\ - 6 r + 10 s + 3 t = - 19 \end{matrix}

See all solutions

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