Question 10.4.3: Evaluating a 3 by 3 Determinant Find the determinant of A = ...
Evaluating a 3 by 3 Determinant
Find the determinant of A=⎣⎢⎡2133−2442−1⎦⎥⎤.
The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.
Learn more on how we answer questions.
Learn more on how we answer questions.
Expanding by the first row, we have ∣A∣=a11A11+a12A12+a13A13, where
A11=(−1)1+1M11=(1)∣∣∣∣∣−242−1∣∣∣∣∣A12=(−1)1+2M12=(−1)∣∣∣∣∣132−1∣∣∣∣∣A13=(−1)1+3M13=(1)∣∣∣∣∣13−24∣∣∣∣∣
Thus,
∣∣∣∣∣∣∣2133−2442−1∣∣∣∣∣∣∣=2(1)∣∣∣∣∣−242−1∣∣∣∣∣+3(−1)∣∣∣∣∣132−1∣∣∣∣∣+4(1)∣∣∣∣∣13−24∣∣∣∣∣
=2(2−8)−3(−1−6)+4(4+6) Evaluate determinants of order 2.
= -12 + 21 + 40 = 49 Simplify.

Related Answered Questions
Question: 10.1.4
Verified Answer:
Linear System
Augmented Matrix
\left\{\be...
Question: 10.4.5
Verified Answer:
First, rewrite the system of equations so that the...
Question: 10.4.1
Verified Answer:
a. \left|\begin{array}{rr}3 & -4 \\1 &a...
Question: 10.3.7
Verified Answer:
For the matrix A, we have
I-A=\left[\begin{...
Question: 10.3.5
Verified Answer:
a. For the matrix A, a=5, b=2, c=4, \text {...
Question: 10.2.10
Verified Answer:
The columns of the product matrix AD represent the...
Question: 10.2.8
Verified Answer:
Because A is of order 2×2 and the order of B is 2×...
Question: 10.2.3
Verified Answer:
a. 3 A=3\left[\begin{array}{rrr}1 & ...
Question: 10.2.2
Verified Answer:
a. Because A and B have the same order, A + B is d...
Question: 10.1.8
Verified Answer:
\left\{\begin{array}{rr}x-y-z= & 1 \\2 ...