# Linear combo

pyroknife
Lets say you have 3 vectors v1, v2,v3. They form a 3x3 matrix.

Let's say you're asked if v3 is a linear combo of the other two vectors.

Rref of the matrix gives
1 0 1
0 1 0
0 0 0

The definition of a Linear combo is v3=c1v1+c2v2 where c1 and c2 are scalars.

Okay do this is where I get con fused . If u look at the above matrix c2=0 which means v3=c1v1. Would that mean its not a linear combination of v2 since c2=0?

Also is 0 a scalar?

Homework Helper
Gold Member
Okay do this is where I get con fused . If u look at the above matrix c2=0 which means v3=c1v1. Would that mean its not a linear combination of v2 since c2=0?

Also is 0 a scalar?
It IS a linear combination. c2 = 0 is allowed. 0 is a scalar.

Mentor
Lets say you have 3 vectors v1, v2,v3. They form a 3x3 matrix.

Let's say you're asked if v3 is a linear combo of the other two vectors.

Rref of the matrix gives
1 0 1
0 1 0
0 0 0
Assuming this is an augmented matrix, you have c1 = 1 and c2 = 0.
The definition of a Linear combo is v3=c1v1+c2v2 where c1 and c2 are scalars.

Okay do this is where I get con fused . If u look at the above matrix c2=0 which means v3=c1v1. Would that mean its not a linear combination of v2 since c2=0?
No, v3 is a linear combination of v1 and v2; namely, v3 = 1v1 + 0v2.
Also is 0 a scalar?
Yes, unless you're talking about a 0 vector, which in this case would be <0, 0, 0>.
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "https://www.physicsforums.com/threads/linear-combo.639002/", "fetch_time": 1675114749000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2023-06/segments/1674764499829.29/warc/CC-MAIN-20230130201044-20230130231044-00401.warc.gz", "warc_record_offset": 961915936, "warc_record_length": 14126, "token_count": 471, "char_count": 1403, "score": 4.1875, "int_score": 4, "crawl": "CC-MAIN-2023-06", "snapshot_type": "latest", "language": "en", "language_score": 0.931755006313324, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00052-of-00064.parquet"}