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Home » I’d Never Guess—One Stick of Butter Is This Much! Watch Also! - Dachbleche24

I’d Never Guess—One Stick of Butter Is This Much! Watch Also! - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 We are given a linear transformation defined by:

📌 \mathbf{M} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} x + 2y \ 3x - y \end{bmatrix}

📌 This implies that \(\mathbf{M}\) transforms \((x, y)\) into \((x + 2y, 3x - y)\). We express this transformation using matrix multiplication:

📌 \mathbf{M} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} a & b \ c & d \end{bmatrix} egin{bmatrix} x \ y \end{bmatrix} = egin{bmatrix} ax + by \ cx + dy \end{bmatrix}

📌 Equating components:

📌 ax + by = x + 2y \quad \Rightarrow \quad a = 1, \; b = 2

📌 cx + dy = 3x - y \quad \Rightarrow \quad c = 3, \; d = -1

📌 Thus, the matrix \(\mathbf{M}\) is:

🔥 Popular Posts

#### 200 m
2x + 3y &= 6 \\
4x - y &= 5
Substitute into the first equation: \(2x + 3(4x - 5) = 6\).
Simplify: \(2x + 12x - 15 = 6\), so \(14x = 21\).
Solve: \(x = 1.5\).
Substitute back to find \(y\): \(y = 4(1.5) - 5 = 1\).
#### \(x = 1.5\), \(y = 1\)
If the sum of the first \(n\) natural numbers is given by \(\frac{n(n+...
Set up the equation: \(\frac{n(n+1)}{2} = 210\).

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