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Chapter 1: Problem 2

Write the zero vector of \(M_{3 \times 4}(F)\).

Short Answer

Expert verified
The zero vector of \(M_{3 \times 4}(F)\) is: \[ \begin{pmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix} \]

Step by step solution

01

Understand the dimensions of the matrix

Since the exercise asks for the zero vector of the matrix space \(M_{3 \times 4}(F)\), the matrix we are creating will have 3 rows and 4 columns.
02

Fill the matrix with zeros

In this step, we need to create a \(3 \times 4\) matrix whose entries are all zeros, since a zero vector is a matrix with all its entries equal to zero. The zero vector of \(M_{3 \times 4}(F)\) is: \[ \begin{pmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix} \] I hope this helps you understand how to find the zero vector of a matrix space!

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Most popular questions from this chapter

For a fixed \(a \in R\), determine the dimension of the subspace of \(\mathrm{P}_{n}(R)\) defined by $\left\\{f \in \mathrm{P}_{n}(R): f(a)=0\right\\}$.

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