If A=[ 1 1 1 1 1 1 1 1 1 ], then A^3 is (a) [ 3

step 1 So in the given question we have a determinant matrix A that is given as 1 -1 -1 -1 -1 -1 and we

If A=[ 1 1 1 1 1 1 1 1 ...

If $A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right]$, then $A^{3}$ is (a) $\left[\begin{array}{lll}3 & 1 & 1 \\ 1 & 3 & 1 \\ 1 & 1 & 3\end{array}\right]$ (b) $\left[\begin{array}{lll}3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3\end{array}\right]$ (c) $\left[\begin{array}{lll}1 & 3 & 3 \\ 3 & 1 & 3 \\ 3 & 3 & 1\end{array}\right]$ (d) $\left[\begin{array}{lll}9 & 9 & 9 \\ 9 & 9 & 9 \\ 9 & 9 & 9\end{array}\right]$

If $A=\left[\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right]$, then $A^{3}$ is
(a) $\left[\begin{array}{lll}3 & 1 & 1 \\ 1 & 3 & 1 \\ 1 & 1 & 3\end{array}\right]$
(b) $\left[\begin{array}{lll}3 & 3 & 3 \\ 3 & 3 & 3 \\ 3 & 3 & 3\end{array}\right]$
(c) $\left[\begin{array}{lll}1 & 3 & 3 \\ 3 & 1 & 3 \\ 3 & 3 & 1\end{array}\right]$
(d) $\left[\begin{array}{lll}9 & 9 & 9 \\ 9 & 9 & 9 \\ 9 & 9 & 9\end{array}\right]$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Matrix Multiplication

Matrix multiplication is the process of combining two matrices by taking the dot product of rows of the first matrix with columns of the second matrix. It forms the basis for many operations in linear algebra, including computing powers of matrices. The process requires that the number of columns in the first matrix matches the number of rows in the second, and it is a fundamental operation that underpins many advanced topics in mathematics and applied sciences.

Matrix Powers

Matrix powers involve multiplying a matrix by itself repeatedly. This operation is similar to exponentiation for numbers but requires careful attention to the non-commutativity of matrix multiplication. Understanding matrix powers is essential for analyzing iterative processes, solving systems of linear differential equations, and exploring dynamics in various mathematical models.

Special Matrices

Special matrices, such as constant matrices (e.g., matrices where all entries are the same), have unique properties that can simplify their analysis. They often exhibit symmetries, have low rank, and their powers can sometimes be determined by patterns or closed-form expressions. Recognizing these properties allows for easier computations and provides deeper insight into the structure of such matrices.

Transcript

Please give Ace some feedback