Cofactors and Minors in Determinants

The video revisits the determinant formula of a matrix, focusing on using the first row as a reference. It explains how to calculate the determinant by multiplying elements with their respective minors and cofactors. The video introduces the concepts of minors and cofactors, explaining their significance and how to calculate them for different matrix elements. It also establishes the relationship between a minor and a cofactor, emphasizing the mathematical operations involved. The video concludes with a promise to explore examples in the next lesson.

What is the reference row used in the determinant formula discussed in the video?

• Third row

• Last row

• First row

• Second row

How is the sign determined for the element 'a11' in the determinant formula?

• By the row number

• By the product of the row and column numbers

• By the column number

• By the sum of the row and column numbers

What operation is performed after excluding the row and column of 'a11'?

• Finding the inverse of the remaining elements

• Finding the determinant of the remaining elements

• Multiplication of remaining elements

• Addition of remaining elements

What is the determinant of the remaining elements after excluding 'a11'?

• a22 times a33 minus a23 times a32

• a22 times a32 minus a23 times a33

• a22 plus a32 minus a23 plus a33

• a22 plus a33 minus a23 plus a32

What is the sign factor for 'a12' in the determinant formula?

• Minus 1 raised to 2 plus 2

• Minus 1 raised to 2 plus 3

• Minus 1 raised to 1 plus 1

• Minus 1 raised to 1 plus 2

What is the determinant of the remaining elements for 'a12'?

• a21 plus a33 minus a23 plus a31

• a21 times a33 minus a23 times a31

• a21 plus a31 minus a23 plus a33

• a21 times a31 minus a23 times a33

What is the determinant of the remaining elements for 'a13'?

• a21 times a32 minus a22 times a31

• a21 plus a32 minus a22 plus a31

• a21 times a31 minus a22 times a32

• a21 plus a31 minus a22 plus a32

What is the sign factor for 'a13' in the determinant formula?

• Minus 1 raised to 1 plus 2

• Minus 1 raised to 2 plus 3

• Minus 1 raised to 1 plus 1

• Minus 1 raised to 1 plus 3

What is the determinant of the remaining elements after excluding 'a13'?

• a21 times a32 minus a22 times a31

• a21 plus a32 minus a22 plus a31

• a21 plus a31 minus a22 plus a32

• a21 times a31 minus a22 times a32

What is the term used for the smaller determinant part associated with an element?

• Inverse

• Cofactor

• Minor

• Adjugate