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[M] In Exercises $37-40$ , determine if the columns of the matrix span $\mathbb{R}^{4} .$$$\left[\begin{array}{rrrrr}{8} & {11} & {-6} & {-7} & {13} \\ {-7} & {-8} & {5} & {6} & {-9} \\ {11} & {7} & {-7} & {-9} & {-6} \\ {-3} & {4} & {1} & {8} & {7}\end{array}\right]$$

Matrix has pivot element in every row hence it spans in $R^{4}$

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 4

The Matrix Equation Ax D b

Introduction to Matrices

Harvey Mudd College

Baylor University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

01:16

[M] In Exercises $37-40$ ,…

03:03

02:00

03:56

In Exercises $5-8,$ determ…

03:35

03:06

11:56

In Exercises 37 and 38, co…

02:49

In Exercises 39-54, find t…

In Exercises 41-44, determ…

All right, so four problem 40 here were given anatomy tricks, which is off four by five. Milkshakes is a form. I find matrix. Let's say, um, it's naming as a matrix eight. So again, we need to find out the real reduced form off a I'll just write it down. Reduced form off, eh? And this is 10 connective seven over 13 and 00 So we have 01 connected, connected to over 13 and zero and zero. They're pro abi's 0001 zero. That's Rowe ISS 000 zero and one. Okay, so if we count the number of people positions, here's one, two, three and four. So we can. So we have people for people columns in this case, Base matrix people columns. So that means rank off, eh? Is for butt and eighties equal to dimension far for so so we can conclude that columns of a it's been our four

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In mathematics, the absolute value or modulus |x| of a real number x is its …

[M] In Exercises $37-40$ , determine if the columns of the matrix span $\mat…

In Exercises $5-8,$ determine if the columns of the matrix form a linearly i…

In Exercises 37 and 38, construct bases for the column space and the null sp…

In Exercises 39-54, find the determinant of the matrix.Expand by cofactors o…

In Exercises 41-44, determine whether the matrix is in row-echelon form. If …

01:37

Show that if $A B$ is invertible, so is $B$

04:21

With $T$ defined by $T(\mathbf{x})=A \mathbf{x},$ find a vector $\mathbf{x}$…

03:33

Unless otherwise specified, assume that all matrices in these exercises are …

02:37

Give a geometric description of $\operatorname{Span}\left\{\mathbf{v}_{1}, \…

02:23

In Exercises $3-8,$ find the $3 \times 3$ matrices that produce the describe…

05:37

Suppose the block matrix $A$ on the left side of (7) is invertible and $A_{1…

06:30

Repeat Exercise $15 : A=\left[\begin{array}{rrr}{1} & {-3} & {-4} \\…

02:01

Suppose the solution set of a certain system of linear equations can be desc…

02:34

Show that the transformation in Exercise 8 is merely a rotation about the or…

02:08

Let $\mathbf{x}=\left[\begin{array}{c}{x_{1}} \\ {x_{2}}\end{array}\right], …

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