In Exercises 1–8 , evaluate the determinant of the given matrix by ( a ) cofactor expansion and ( b ) using elementary row operations to intro-duce zeros into the matrix. [ − 4 2 3 3 ]
In Exercises 1–8 , evaluate the determinant of the given matrix by ( a ) cofactor expansion and ( b ) using elementary row operations to intro-duce zeros into the matrix. [ − 4 2 3 3 ]
In Exercises 1–8, evaluate the determinant of the given matrix by (a) cofactor expansion and (b) using elementary row operations to intro-duce zeros into the matrix.
[
−
4
2
3
3
]
(a)
Expert Solution
To determine
The determinant of the matrix A=[−4233], using cofactor expansion.
Answer to Problem 1SE
The determinant of the matrix A=[−4233] is −18_.
Explanation of Solution
Definition used:
Determinant:
“The determinant of a matrix A=[abcd] is given by the formula ad−bc and the matrix A is said to be invertible if, ad−bc≠0.”
Calculation:
The given matrix is A=[−4233].
Use cofactor expansion and obtain the value of the determinant as shown below.
det(A)=(−4)⋅3−2⋅3=−12−6=−18
Thus, the determinant of the matrix A=[−4233] is −18_.
(b)
Expert Solution
To determine
The determinant of the matrix A=[−4233], using elementary row operations.
Answer to Problem 1SE
The determinant of the matrix A=[−4233] is −18_.
Explanation of Solution
The given matrix is A=[−4233].
Obtain the value of the determinant as shown below.
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HOW TO FIND DETERMINANT OF 2X2 & 3X3 MATRICES?/MATRICES AND DETERMINANTS CLASS XII 12 CBSE; Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=bnaKGsLYJvQ;License: Standard YouTube License, CC-BY