What is the trace of a matrix? Calculate the trace of a 3x3 identity matrix
Question
What is the trace of a matrix? Calculate the trace of a 3x3 identity matrix
Solution
The trace of a matrix is the sum of the elements on its main diagonal (from top left to bottom right).
For a 3x3 identity matrix, the main diagonal consists of the elements 1, 1, and 1 (since an identity matrix has 1's on the main diagonal and 0's everywhere else).
So, to calculate the trace, you simply add these elements together:
1 + 1 + 1 = 3
Therefore, the trace of a 3x3 identity matrix is 3.
Similar Questions
What is the trace of a matrix?a.The sum of all elements.b.The product of the diagonal elements.c.The difference of the diagonal elements.d.The sum of the diagonal elements
Check you answer by computing C = AB − I, where I is the identity matrix
Let R=⎛⎝x000y000z⎞⎠ be a non-zero 3×3 matrix, where xsinθ=ysin(θ+2π3)=zsin(θ+4π3) ≠0,θ∈(0,2π). For a square matrix M, let trace (M) denote the sum of all the diagonal entries of M. Then, among the statements:(I) Trace (R)=0(II) If trace (adj(adj(R))=0, then R has exactly one non-zero entry.
Determine the eigenvalues of the matrix[ 3 1 ] [1 2 ]
Steps to solve Inverse of a 3x3 matrix/
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