SECTION B INSTRUCTION: Answer Any 6 Questions. (a) Find the value of y if | 1-1, 2|= -4 (b) Show the interval in which x must be to satisfy the inequalities 2x+5>=1 and 2x-4<=2

The determinant of a $2 \times 2$ matrix $\begin{vmatrix} a & b \\ c & d \end{vmatrix}$ is given by $ad - bc$.
Given the equation $\begin{vmatrix} y-1 & 2 \\ 4 & 3 \end{vmatrix} = -4$, we set up the determinant:

$$(y-1)(3) - (2)(4) = -4$$ $$3y - 3 - 8 = -4$$ $$3y - 11 = -4$$

Add 11 to both sides of the equation:

$$3y = -4 + 11$$ $$3y = 7$$

Divide by 3:

$$y = \frac{7}{3}$$

The value of $y$ is $\boxed{\frac{7}{3}}$.

Given the inequality $2x+5 \ge 1$:

$$2x \ge 1 - 5$$ $$2x \ge -4$$ $$x \ge \frac{-4}{2}$$ $$x \ge -2$$

Given the inequality $\frac{x}{3} < 4$:

$$x < 4 \times 3$$ $$x < 12$$

We need $x$ to satisfy both $x \ge -2$ and $x < 12$.
This means $x$ is greater than or equal to -2 and less than 12.
The interval is expressed as:

$$[-2, 12)$$

The interval in which $x$ must be is $\boxed{[-2, 12)}$.