PLEASE do both!!! I WILL give thumbs up!! Pleaseee On this educational page, we will explore some concepts in linear algebra, specifically in the context of vector spaces and linear combinations.---**Given:**Matrix \( A \) and vector \( b \)\[ A = \begin{bmatrix} 1 & 0 & -6 \\0 & 3 & -5 \\-5 & 9 & 4 \end{bmatrix} \quad \text{and} \quad b = \begin{bmatrix} 9 \\-2 \\-29 \end{bmatrix} \]**Columns of \( A \)**Let's denote the columns of \( A \) by \( \mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3 \). Define \( W \) as the span of these columns:\[ W = \text{Span} \{ \mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3 \} \]**Questions:**1. Is \( b \) in \(\{ \mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3 \}\)? How many vectors are in \(\{ \mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3 \}\)? 2. Is \( b \) in \( W \)? How many vectors are in \( W \)?3. Show that \( \mathbf{a}_2 \) is in \( W \). [Hint: Row operations are unnecessary.]---### Detailed Problem Solvinga. **Is \( b \) in \(\{ \mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3 \}\)?**Select the correct choice below and, if necessary, fill in the answer box to complete your choice.- \( \mathbf{A.} \) No, \( b \) is not in \(\{ \mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3 \}\) since \( b \) is not equal to \( \mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3 \).- \( \mathbf{B.} \) Yes, \( b \) is in \(\{ \mathbf{a}_1, \mathbf{a}_ ### Linear Combinations of VectorsUse the accompanying figure to write each vector listed as a linear combination of \( u \) and \( v \).**Vectors:**- \( b \)- \( w \)- \( x \)- \( y \)#### Explanation of Diagram:The diagram is a Cartesian plane with vectors \( u \) and \( v \) depicted along with their multiples and combinations. The vectors of interest (\( b \), \( w \), \( x \), and \( y \)) are marked on the grid. Each marked point on the grid corresponds to a particular linear combination of the basis vectors \( u \) and \( v \).Here are the markers of different vectors:- \(O\) represents the origin (0,0).- \(u\) and \(v\) represent the unit vectors in the directions of \(u\) and \(v\), respectively.- Other points are arranged in a grid based on multiples and sums of these basis vectors.#### Write Vector **b** as a Linear CombinationWrite \( b \) as a linear combination of \( u \) and \( v \):\[ b = (\underline{\hspace{1cm}}) u + (\underline{\hspace{1cm}}) v \]>(*Type integers or decimals.)*

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10-6 03-5 and b -59 4 a. Is b in (a, a, a)? How many vectors are in (a,. a. az)? b. Is b in W? How many vectors are in W? c. Show that az is in W. (Hint: Row operations are unnecessary.] Let A Denote the columns of A by a₁. 2. 3. and let W-Span (₁, 2, 3). a. Is b in (a,, a2. a)? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. No, b is not in (a,. a2. a), since b is not equal to a,, a2, or ag. B. Yes, b is in (a,. a2. a) since ba (Type a whole number.) C. Yes, b is in (a,. a2. a3), since, although b is not equal to a,. a2. or ay, it can be expressed as a linear combination of them. In particular, b= (a₁ + a₂ + (ªz. (Simplify your answers.) D. No, b is not in (a, a, a) since it cannot be generated by a linear combination of a,, a2, and a.