Get expert advice and community support on IDNLearn.com. Get comprehensive answers to all your questions from our network of experienced experts.
Sagot :
Let's determine the determinants of the given matrices [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex].
Given matrices:
[tex]\[ A = \begin{pmatrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{pmatrix} \][/tex]
[tex]\[ B = \begin{pmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{pmatrix} \][/tex]
[tex]\[ C = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{pmatrix} \][/tex]
1. Determinant of Matrix [tex]\(A\)[/tex]:
[tex]\[ A = \begin{pmatrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{pmatrix} \][/tex]
After calculating the determinant, we find:
[tex]\[ \det(A) = 1 \][/tex]
2. Determinant of Matrix [tex]\(B\)[/tex]:
[tex]\[ B = \begin{pmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{pmatrix} \][/tex]
After calculating the determinant, we find:
[tex]\[ \det(B) = 2 \][/tex]
3. Determinant of Matrix [tex]\(C\)[/tex]:
[tex]\[ C = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{pmatrix} \][/tex]
After calculating the determinant, we find:
[tex]\[ \det(C) = 0 \][/tex]
Thus, the determinants of the matrices [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex] are [tex]\( 1 \)[/tex], [tex]\( 2 \)[/tex], and [tex]\( 0 \)[/tex] respectively.
Given matrices:
[tex]\[ A = \begin{pmatrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{pmatrix} \][/tex]
[tex]\[ B = \begin{pmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{pmatrix} \][/tex]
[tex]\[ C = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{pmatrix} \][/tex]
1. Determinant of Matrix [tex]\(A\)[/tex]:
[tex]\[ A = \begin{pmatrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{pmatrix} \][/tex]
After calculating the determinant, we find:
[tex]\[ \det(A) = 1 \][/tex]
2. Determinant of Matrix [tex]\(B\)[/tex]:
[tex]\[ B = \begin{pmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{pmatrix} \][/tex]
After calculating the determinant, we find:
[tex]\[ \det(B) = 2 \][/tex]
3. Determinant of Matrix [tex]\(C\)[/tex]:
[tex]\[ C = \begin{pmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{pmatrix} \][/tex]
After calculating the determinant, we find:
[tex]\[ \det(C) = 0 \][/tex]
Thus, the determinants of the matrices [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex] are [tex]\( 1 \)[/tex], [tex]\( 2 \)[/tex], and [tex]\( 0 \)[/tex] respectively.
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Your search for answers ends at IDNLearn.com. Thanks for visiting, and we look forward to helping you again soon.