If 𝐛1=[ -2 -6 3 -1 -2 ] and 𝐛2=[ -4 -6 0 0

Name: Problem 18, Chapter 2: Differential Equations and Linear Algebra
Uploaded: 2020-05-10T11:49:08-08:00
Duration: 1 min 11 s
Channel: Nez Nikoo
Description: If 𝐛1=[ -2 -6 3 -1 -2 ] and 𝐛2=[ -4 -6 0 0 1 ] write the matrix B=[𝐛1, 𝐛2], and determine the row vectors of B.

step 1 Okay, the problem is giving us two columns. So there's two column vectors and it's asking us to

Question

If $$\mathbf{b}_{1}=\left[\begin{array}{r}-2 \\-6 \\3 \\-1 \\-2\end{array}\right] \quad \text { and } \quad \mathbf{b}_{2}=\left[\begin{array}{r}-4 \\-6 \\0 \\0 \\1\end{array}\right]$$ write the matrix $B=\left[\mathbf{b}_{1}, \mathbf{b}_{2}\right],$ and determine the row vectors of $B$.

   If
$$\mathbf{b}_{1}=\left[\begin{array}{r}-2 \\-6 \\3 \\-1 \\-2\end{array}\right] \quad \text { and } \quad \mathbf{b}_{2}=\left[\begin{array}{r}-4 \\-6 \\0 \\0 \\1\end{array}\right]$$
write the matrix $B=\left[\mathbf{b}_{1}, \mathbf{b}_{2}\right],$ and determine the row vectors of $B$.

Differential Equations and Linear Algebra

Stephen W. Goode,… 4th Edition

Chapter 2, Problem 18

Instant Answer

Solved by Expert Nez Nikoo

05/10/2020

Step 1

We are asked to form a matrix $B$ using these vectors as columns. This can be done by simply placing the vectors side by side. So, the matrix $B$ is given by $$B=\left[\mathbf{b}_{1}, \mathbf{b}_{2}\right]=\left[\begin{array}{rr}-2 & -4 \\-6 & -6 \\3 & 0 \\-1 & 0 Show more…

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If $$\mathbf{b}_{1}=\left[\begin{array}{r}-2 \\-6 \\3 \\-1 \\-2\end{array}\right] \quad \text { and } \quad \mathbf{b}_{2}=\left[\begin{array}{r}-4 \\-6 \\0 \\0 \\1\end{array}\right]$$ write the matrix $B=\left[\mathbf{b}_{1}, \mathbf{b}_{2}\right],$ and determine the row vectors of $B$.

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Key Concepts

Matrix Construction from Column Vectors

This concept involves forming a matrix by arranging given vectors as columns. Each column in the matrix corresponds to one of the provided vectors, aligning their elements in a structured way. It is a common approach to represent a set of vectors where each vector's entries fill the corresponding column positions in the matrix.

Row Vectors

Row vectors of a matrix are the horizontal components that result from each row of the matrix. Once the matrix is constructed from its columns, the row vectors are simply the sequences of entries that appear in each row when read from left to right. They are essential in various linear algebra operations, including defining systems of equations and studying the matrix's properties.

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