[amp_mcq option1=”[p, q, r] = [b, a, c]” option2=”[p, q, r] = [b, c, a]” option3=”[p, q, r] = [c, a, b]” option4=”[p, q, r] = [c, b, a]” correct=”option1″]<\/p>\n
The correct answer is $\\boxed{\\text{(C)}}$.<\/p>\n
Let’s start by simplifying the given equation. We can factor out a $1\/3$ from the third column of the matrix on the right-hand side, so we get:<\/p>\n
$$\\left[ {\\begin{array}{{20}{c}} a \\ b \\ c \\end{array}} \\right] = \\frac{1}{3} \\left[ {\\begin{array}{<\/em>{20}{c}} 1&1&1 \\ 1&{W_3^1}&{W_3^2} \\ 1&{W_3^2}&{W_3^4} \\end{array}} \\right]\\left[ {\\begin{array}{{20}{c}} 1 \\ {W_3^2} \\ {W_3^4} \\end{array}} \\right]\\left[ {\\begin{array}{<\/em>{20}{c}} {A} \\ {B} \\ {C} \\end{array}} \\right]$$<\/p>\n Now, let’s define a new matrix $M$ as follows:<\/p>\n $$M = \\frac{1}{3} \\left[ {\\begin{array}{{20}{c}} 1&1&1 \\ 1&{W_3^1}&{W_3^2} \\ 1&{W_3^2}&{W_3^4} \\end{array}} \\right]\\left[ {\\begin{array}{<\/em>{20}{c}} 1 \\ {W_3^2} \\ {W_3^4} \\end{array}} \\right]$$<\/p>\n Then, we can rewrite the equation as follows:<\/p>\n $$\\left[ {\\begin{array}{{20}{c}} a \\ b \\ c \\end{array}} \\right] = M \\left[ {\\begin{array}{<\/em>{20}{c}} {A} \\ {B} \\ {C} \\end{array}} \\right]$$<\/p>\n This means that the sequences [p, q, r] and [a, b, c] are related by the matrix $M$. In other words, if we multiply the sequence [a, b, c] by the matrix $M$, we get the sequence [p, q, r].<\/p>\n Now, let’s look at the options. Option A says that [p, q, r] = [b, a, c]. This is not possible, because the first element of [p, q, r] is $p$, which is equal to $a$. However, the first element of [b, a, c] is $b$. Therefore, option A is not correct.<\/p>\n Option B says that [p, q, r] = [b, c, a]. This is also not possible, because the second element of [p, q, r] is $q$, which is equal to $b$. However, the second element of [b, c, a] is $c$. Therefore, option B is also not correct.<\/p>\n Option C says that [p, q, r] = [c, a, b]. This is possible, because the first element of [p, q, r] is $p$, which is equal to $a$. The second element of [p, q, r] is $q$, which is equal to $b$. And the third element of [p, q, r] is $r$, which is equal to $c$. Therefore, option C is correct.<\/p>\n Option D says that [p, q, r] = [c, b, a]. This is not possible, because the third element of [p, q, r] is $r$, which is equal to $c$. However, the third element of [c, b, a] is $a$. Therefore, option D is also not correct.<\/p>\n In conclusion, the correct answer is $\\boxed{\\text{(C)}}$.<\/p>\n","protected":false},"excerpt":{"rendered":" [amp_mcq option1=”[p, q, r] = [b, a, c]” option2=”[p, q, r] = [b, c, a]” option3=”[p, q, r] = [c, a, b]” option4=”[p, q, r] = [c, b, a]” correct=”option1″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[959],"tags":[],"class_list":["post-54045","post","type-post","status-publish","format-standard","hentry","category-signal-processing","no-featured-image-padding"],"yoast_head":"\n