problem archive
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Find the solution to the system of equations: $3x - 2y = 5$, $2x + y = 8$ -
Factor the quadratic expression: $x^2 - 6x + 9$ -
Calculate the dot product of vectors $\mathbf{u} = \langle 1, -2, 3 \rangle$ and $\mathbf{v} = \langle -1, 4, 2 \rangle$ -
Solve for x: $2x + 3 = 7$ -
Multiply the matrices: $A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix}$, $B = \begin{bmatrix} 5 & 0 \\ -2 & 1 \end{bmatrix}$ -
Apply the linear transformation $T(x, y) = (2x + y, 3x - y)$ to the vector $\langle 1, 2 \rangle$ -
Solve for x: $4x - 6 = 2$ -
Find the inverse of matrix $C = \begin{bmatrix} 2 & 1 \\ 3 & 4 \end{bmatrix}$ -
Find the solution to the system of equations: $2x + 3y = 10$, $3x - y = 4$ -
Determine the eigenvalues and eigenvectors of matrix $D = \begin{bmatrix} 3 & 1 \\ 1 & 2 \end{bmatrix}$ -
Factor the quadratic expression: $2x^2 - 5x + 2$ -
Multiply the matrices: $A = \begin{bmatrix} 3 & 2 \\ -1 & 4 \end{bmatrix}$, $B = \begin{bmatrix} 5 & 1 \\ 2 & -3 \end{bmatrix}$ -
Calculate the dot product of vectors $\mathbf{u} = \langle -1, 2, -3 \rangle$ and $\mathbf{v} = \langle 4, -1, 2 \rangle$ -
Apply the linear transformation $T(x, y) = (3x - y, 2x + y)$ to the vector $\langle 2, -1 \rangle$ -
Find the inverse of matrix $E = \begin{bmatrix} 2 & 0 \\ -1 & 3 \end{bmatrix}$ -
Find the solution to the system of equations: $2x - 3y = -5$, $4x + y = 7$ -
Determine the eigenvalues and eigenvectors of matrix $F = \begin{bmatrix} 4 & 2 \\ 1 & 5 \end{bmatrix}$ -
Solve for x: $-3x + 7 = 4$ -
Factor the quadratic expression: $x^2 + 5x + 6$ -
Multiply the matrices: $A = \begin{bmatrix} 1 & -2 \\ 3 & 4 \end{bmatrix}$, $B = \begin{bmatrix} 2 & 1 \\ -1 & 0 \end{bmatrix}$