It seems like the image you uploaded contains math problems written in a non-English script (most likely Armenian). From what I can interpret, it seems that these are linear algebra problems involving vector equations or linear combinations of vectors, particularly involving vectors $\vec{a}$, $\vec{b}$, and scalar multiples.

Here’s what I can generally infer:

Problem 47:

• It seems to discuss a condition about the linear combination of vectors $\vec{a}$ and $\vec{b}$, with some scalar factors like $x - 1$ and other expressions like $3a + xb$. This could imply something related to vector dependence or span.

Problem 48:

• The structure of the equations involving terms like $\lambda \vec{a} + \vec{b}$ and $\nu \vec{a} + \lambda \vec{b}$ suggests it's dealing with a system of linear equations involving vectors, likely focused on solving for $\lambda$, $\nu$, or a condition for linear dependence.

If you would like, I can help translate or clarify this further. You can also provide more context about the problem, and I can assist with the math.

Would you like me to analyze one of these problems in more detail, or help you solve them step-by-step?

5 related questions to expand:

1. What do you understand by a linear combination of vectors?
2. How can we determine if two vectors are linearly dependent?
3. What role do scalars like $\lambda$ and $\nu$ play in vector equations?
4. How would you solve a system of vector equations?
5. What is the geometric interpretation of vector linear dependence?

Tip: In vector algebra, determining if a set of vectors are linearly dependent often involves checking if one vector can be written as a scalar multiple or combination of others.