# Tr(A) – Tr(B) has value equal to:

Let

$$\begin{array}{l}A+2B=\begin{bmatrix} 1&2 &0 \\ 6&-3 &3 \\ -5&3 &1 \end{bmatrix}\end{array}$$
and
$$\begin{array}{l}2A-B=\begin{bmatrix} 2&-1 &5 \\ 2&-1 &6 \\ 0&1 &2 \end{bmatrix}\end{array}$$
. If Tr(A) denotes the sum of all diagonal elements of the matrix A, then Tr(A) – Tr(B) has value equal to:

a. 0

b. 1

c. 3

d. 2

Solution:

tr (A + 2B) ≡ tr (A) + 2 tr (B) = –1 …..(1)

and tr (2A – B) ≡ 2tr (A) – tr (B) = 3 …..(2)

On solving (1) and (2) we get

tr (A) = 1, tr(B) = –1

tr (A) – tr(B) = 1 + 1 = 2
{"found_math": true, "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": 1, "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://byjus.com/jee-questions/tra-minus-trb-has-value-equal-to/", "fetch_time": 1653316427000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2022-21/segments/1652662558030.43/warc/CC-MAIN-20220523132100-20220523162100-00380.warc.gz", "warc_record_offset": 199208055, "warc_record_length": 155468, "token_count": 274, "char_count": 553, "score": 4.0625, "int_score": 4, "crawl": "CC-MAIN-2022-21", "snapshot_type": "latest", "language": "en", "language_score": 0.5988214612007141, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00030-of-00064.parquet"}