🧮 algebra

1. Calculate the difference of the two matrices element-wise: $$\begin{bmatrix}2 & -3 \\ -4 & 2\end{bmatrix} - \begin{bmatrix}-1 & -5 \\ 3 & -2\end{bmatrix} = \begin{bmatrix}2 - (-

1. **Tenglama:** $$3^{2\log x} = 16$$ 2. **Formulalar:** $$a^{\log_b c} = c^{\log_b a}$$ va $$16 = 2^4$$

1. **State the problem:** Solve for $x$ in the equation $70 = 42 + 25 - 6 + x$. 2. **Combine like terms on the right side:**

1. Problem: Solve the equation $\lg(x^2 + 2x - 3) = \lg(x - 3)$. 2. Since $\lg a = \lg b$ implies $a = b$ (for $a,b > 0$), we set:

1. The problem is to solve the equation $2. q$. 2. However, the expression $2. q$ is incomplete and does not form a solvable equation or expression as given.

1. The problem asks to put a system of equations into matrix form and solve parts a), b), c), and d). Since the exact system is not provided, I will demonstrate the general process

1. **State the problem:** Simplify the expression $$\left(\frac{3x^4}{y}\right)^{-3}$$. 2. **Recall the rule for negative exponents:** For any nonzero expression $a$, $$a^{-n} = \f

1. The problem states: If a polynomial $f(x)$ is divided by $(x - a)$, then the remainder of the division is equal to $f(a)$. 2. This is a statement of the Remainder Theorem, which

1. **Stating the problem:** Diberikan deret geometri dengan suku pertama $a$ dan pembanding $r = 2 \log(x - 3)$. Kita diminta menentukan hubungan antara kuantitas P (nilai $x$ yang

1. The problem is to solve the equation shown in the image: $$\frac{2x+3}{x-1} = 4$$. 2. The formula used here is to solve rational equations by eliminating the denominator: multip

1. The user asked for examples, but no specific math problem was given. 2. Since no specific problem is stated, I will provide a simple algebra example to illustrate solving an equ

1. The problem is to sketch the graph of a function, but no specific function is given. 2. To sketch a graph, we need the function's equation or description.

1. **Problem statement:** Complete the matrix equality: $$\begin{bmatrix} 2 & 7 - a & 8 \\ -5 & 20 & 20b \end{bmatrix} = \begin{bmatrix} 2 & -12 & 8 \\ -5 & c + 25 & 100 \end{bmatr

1. **Nyatakan masalah:** Diberikan grup matriks invertibel 2x2 $\langle M_2^*, \times \rangle$ dan grup bilangan real tidak nol $\langle \mathbb{R}^*, \times \rangle$. Diberikan pe

1. The problem is to understand the properties of rational exponents and how they relate to integral exponents. 2. The key formula is that for positive real numbers $a$ and $b$, an

1. **State the problem:** Solve the linear equation $2x + y = 1$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, subtract $2x$ from both sides of the equation.

1. **State the problem:** Simplify or analyze the expression $2x + y + 1$. 2. **Understand the expression:** This is a linear expression in two variables $x$ and $y$ with a constan

1. The problem is to find the limit as $n$ approaches infinity of the sequence $$1 + 2 + 2^2 + \dots + 2^{n-1} - 3 \cdot 2^{n+1}.$$\n\n2. This is a sum of a geometric series minus

1. **Тодорхойлолт:** $\lim_{n \to \infty} 1 + 2 + 2^2 + \dots + 2^{n-1} - 3 \cdot 2^{n+1}$ дарааллын хязгаарыг олох. 2. **Формул ба дүрэм:** Геометр прогрессын нийлбэрийн томъёо аш

1. **State the problem:** We know the car's value in 2021 is 16000 and it depreciates by 12.5% each year. We want to find its value in 2016. 2. **Formula used:** The value after $t

1. Stating the problem: Solve the system of linear equations using Gaussian elimination: $$\begin{cases} x_1 + 4x_2 + 2x_3 = 20 \\ -x_1 - 5x_2 + 3x_3 = -24 \\ 3x_1 - 3x_2 + 4x_3 =