Chapter 4: Q 4.89 (page 447)

Evaluate the determinant
(a) $[\begin{matrix} 5 & - 3 \\ 2 & - 4 \end{matrix}]$ (b) $[\begin{matrix} - 4 & - 6 \\ 0 & 7 \end{matrix}]$

Short Answer

Expert verified

Part (a) The value of the determinant is -14.

Part (b) The value of the determinant is -28.

Step by step solution

Part (a). Step 1. Given information

The given determinant is $[\begin{matrix} 5 & - 3 \\ 2 & - 4 \end{matrix}]$ .

Part (a) Step 2. Calculation.

Firstly write the determinant

$[\begin{matrix} 5 & - 3 \\ 2 & - 4 \end{matrix}]$

Subtract the products of the diagonals

localid="1658971311759" $= (5 \times - 4) - (- 3 \times 2) = - 20 - (- 6) = - 14$

Hence the determinant value is -14.

Part (b) Step 1.Given information.

The given determinant is $[\begin{matrix} - 4 & - 6 \\ 0 & 7 \end{matrix}]$

Part (b) Step 2. Calculation

Firstly write the determinant.

[\begin{matrix} - 4 & - 6 \\ 0 & 7 \end{matrix}]

Subtract the products of the diagonals.

$= (7 \times - 4) - (0 \times - 6) = - 28 + 0 = - 28$

Hence the determinant value is -28.

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Evaluate the determinant
(a) $[\begin{matrix} 5 & - 3 \\ 2 & - 4 \end{matrix}]$ (b) $[\begin{matrix} - 4 & - 6 \\ 0 & 7 \end{matrix}]$

Short Answer

Step by step solution

Part (a). Step 1. Given information

Part (a) Step 2. Calculation.

Part (b) Step 1.Given information.

Part (b) Step 2. Calculation

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Short Answer

Step by step solution

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Evaluate the determinant
(a) $[\begin{matrix} 5 & - 3 \\ 2 & - 4 \end{matrix}]$ (b) $[\begin{matrix} - 4 & - 6 \\ 0 & 7 \end{matrix}]$