Q46.
Question
Question: CRITICAL THINKING
Make a conjecture about how you could find the determinant of a matrix using the expansion by minors method. Use a diagram in your explanation.
Step-by-Step Solution
VerifiedA four order determinant is
For a determinant of order 4, minors are determinant of order 3. On expanding four order determinant by first row minors are
To expand the determinant, multiply the minors with positive or negative sign as shown in the following image
In the above image position signs alternate between positive and negative, beginning with a positive sign in first row, first column.
Determinant of order 4 is multiply a row number with its minor and position sign, then add the terms with positive position sign and then subtract negative position sign terms from it as shown below
A four order determinant is determinant of a square matrix of order 4.
It can be written as
For a determinant of order 4, minors are determinant of order 3. On expanding four order determinant by first row minors are
To expand the determinant, multiply the minors with positive or negative sign as shown in the following image
In the above image position signs alternate between positive and negative, beginning with a positive sign in first row, first column.
Determinant of order 4 is multiply a row number with its minor and position sign, then add the terms with positive position sign and then subtract negative position sign terms from it as shown below