Question

Find bases for the null space, the row space and the column space for the 4 X 5 matrix 1 2 1 0 2 2 3 3 -2 1 3 4 5 -3 -1 1 3 0 2 5 Express any column vector of the matrix, which not in the basis of the column space, as a linear combination of the vectors of the basis.

Name: find bases for the null space the row space and the column space for the 4 x 5 matrix 1 2 1 0 2 2 3 3 2 1 3 4 5 3 1 1 3 0 2 5 express any column vector of the matrix which not in the basis o 44495
Uploaded: 2022-06-02T14:29:31-08:00
Duration: 6 min 19 s
Channel: Shaiju T
Description: find bases for the null space the row space and the column space for the 4 x 5 matrix 1 2 1 0 2 2 3 3 2 1 3 4 5 3 1 1 3 0 2 5 express any column vector of the matrix which not in the basis o 44495

          Find bases for the null space, the row space and the column
space for the 4 X 5 matrix
1    2    1    0   
2
2    3    3   -2   
1
3    4    5   -3 
 -1
1    3    0    2   
5
Express any column vector of the matrix,  which not in
the basis of the column space,  as a linear combination of the
vectors of the basis.

Added by Robert E.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shaiju T

06/02/2022

Step 1

From the row reduced form of B, we have the following equations: \[ x_1 + 2x_2 + x_3 + 2x_5 = 0 \] \[ -x_2 + x_3 - 2x_4 - x_5 = 0 \] \[ x_4 - x_5 = 0 \] Let \( x_5 = t \) be a free variable, then we can express the other variables in terms of \( t \): \[ x_4 = t Show more…

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Find bases for the null space, the row space and the column space for the 4 X 5 matrix 1 2 1 0 2 2 3 3 -2 1 3 4 5 -3 -1 1 3 0 2 5 Express any column vector of the matrix, which not in the basis of the column space, as a linear combination of the vectors of the basis.