📘 linear algebra

1. **Stating the problem:** Find the eigenvalues of the matrix $$A = \begin{pmatrix}4 & 6 & 6 \\ 1 & 3 & 2 \\ -1 & -5 & -2 \end{pmatrix}$$ given that two eigenvalues are equal and

1. The problem asks to find the eigenvalues of the matrix \( A = \begin{pmatrix} 3 & 2 & 1 \\ 0 & 4 & 2 \\ 0 & 0 & 1 \end{pmatrix} \) and then find the eigenvalues of the adjoint m

1. The problem asks for the resulting matrix when multiplying two 3x2 matrices. 2. Matrix multiplication is defined only when the number of columns in the first matrix equals the n

1. **State the problem:** Find a matrix $P$ that diagonalizes the matrix $$ A = \begin{bmatrix} 1 & 0 & 1 \\ 1 & 0 & 1 \\ 1 & 0 & 1 \end{bmatrix} .$$

1. The problem is to find the matrix \(A\) given that \(4A = \begin{pmatrix} 4 & -8 & 13 \\ ... & ... & ... \\ ... & ... & ... \end{pmatrix}\).\n\n2. To find \(A\), we divide each

1. **Problem:** Investigate the linear dependence of the vectors \( X_1 = [1,2,-1,3], X_2 = [2,-1,3,2], X_3 = [-1,8,-9,5] \) and if possible, find a relation between them. 2. To ch

1. Problem: Show regularity and find inverse of the transformation with $$A=\begin{bmatrix}2&1&1\\1&1&-1\\1&2&0\end{bmatrix}$$ and $Y=AX$. 2. Compute determinant of $A$.

1. We are asked to find the inverse of the matrix $$\begin{bmatrix}8 & 4 & 3 \\ 2 & 1 & 1 \\ 1 & 2 & 2\end{bmatrix}$$.

1. Problem: Find matrix $A$ given $A + 2B = C$, with $B = \begin{bmatrix}1 & 2 & 2 \\ 0 & 2 & -1\end{bmatrix}$ and

1. Problem: Find AB and BA for the given matrices A and B if they are defined. **a)**

1. The problem appears to involve understanding the matrix \( \begin{bmatrix} a & b \\ c & d \end{bmatrix} \). 2. This is a general 2x2 matrix with elements \(a, b, c, d\).

1. **State the Problem:** We have four 3x3 matrices given as follows: Question 1.1: Matrix B = $$\begin{bmatrix}7 & 1 & 3 \\ 6 & 7 & 0 \\ 0 & 5 & 4\end{bmatrix}$$

1. Find the determinant of the given matrices. **i.** Calculate the determinant of matrix

1. We are asked to multiply a 3x3 matrix by a 3x1 vector. The matrix is: $$\begin{bmatrix}-600c & -120c & -144c \\ -442y & -234y & -104y \\ -180z & -260z & 240z\end{bmatrix}$$

1. Let's define the problem clearly: solving a matrix usually means finding solutions to a system of linear equations represented by the matrix or finding its inverse or determinan

1. The problem involves multiplying a 3x3 matrix: $$\begin{bmatrix}-60 & -12 & 144 \\ -442 & -234 & -104 \\ -180 & -260 & 240\end{bmatrix}$$

1. The problem is to multiply two 3x3 matrices: Matrix A = \( \begin{bmatrix}8 & 2 & 5 \\ 1 & 2 & 2 \\ 0 & 4 & 3 \end{bmatrix} \) and Matrix B = \( \begin{bmatrix}1 & 6 & 2 \\ 7 &

1. The term "determination" likely refers to the "determinant" in a mathematical context. 2. To find the determinant, you need to provide a matrix or a specific system.

1. Problem Statement: You mentioned having a linear algebra question, but please provide the specific problem or concept you'd like help with. 2. Explanation: Linear algebra covers

1. Stating the problem: Solve the system of linear equations using Cramer's rule: $$-5x + 9y - 7y = 0$$

1. Given the problem involves multiple subproblems related to matrices and systems of equations, we will address each question briefly but with clear steps. 2. Problem0.16: Verify