Connect with knowledgeable individuals and find the best answers at IDNLearn.com. Our platform is designed to provide trustworthy and thorough answers to any questions you may have.
Sagot :
To determine the value of [tex]\( a \)[/tex] that makes the matrix
[tex]\[ \begin{pmatrix} a & 0 \\ 0 & a \end{pmatrix} \][/tex]
an identity matrix, we first need to understand what an identity matrix is.
An identity matrix is a special type of matrix in which all the elements on the main diagonal are 1, and all other elements are 0. In the context of a 2x2 identity matrix, it is represented as
[tex]\[ \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \][/tex]
Comparing this with the given matrix
[tex]\[ \begin{pmatrix} a & 0 \\ 0 & a \end{pmatrix} \][/tex]
we observe that for this matrix to be equivalent to the identity matrix, the entries on the main diagonal must both be equal to 1. Therefore, we need both instances of [tex]\( a \)[/tex] in the matrix to be 1.
This means:
[tex]\[ a = 1 \][/tex]
So, the value of [tex]\( a \)[/tex] that makes the given matrix an identity matrix is [tex]\( \boxed{1} \)[/tex].
[tex]\[ \begin{pmatrix} a & 0 \\ 0 & a \end{pmatrix} \][/tex]
an identity matrix, we first need to understand what an identity matrix is.
An identity matrix is a special type of matrix in which all the elements on the main diagonal are 1, and all other elements are 0. In the context of a 2x2 identity matrix, it is represented as
[tex]\[ \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \][/tex]
Comparing this with the given matrix
[tex]\[ \begin{pmatrix} a & 0 \\ 0 & a \end{pmatrix} \][/tex]
we observe that for this matrix to be equivalent to the identity matrix, the entries on the main diagonal must both be equal to 1. Therefore, we need both instances of [tex]\( a \)[/tex] in the matrix to be 1.
This means:
[tex]\[ a = 1 \][/tex]
So, the value of [tex]\( a \)[/tex] that makes the given matrix an identity matrix is [tex]\( \boxed{1} \)[/tex].
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find clear answers at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.