Uncover valuable information and solutions with IDNLearn.com's extensive Q&A platform. Discover reliable and timely information on any topic from our network of experienced professionals.
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].
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.