{"id":20009,"date":"2024-04-15T05:47:09","date_gmt":"2024-04-15T05:47:09","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=20009"},"modified":"2024-04-15T05:47:09","modified_gmt":"2024-04-15T05:47:09","slug":"consider-the-matrices-x4-a%c2%97-3-y4-a%c2%97-3-and-p2-a%c2%97-3-the-order-of-pxty-1-ptt-will-be-a-2-a%c2%97-2-b-3-a%c2%97-3-c-4-a%c2%97-3-d-3-a%c2%97-4","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/consider-the-matrices-x4-a%c2%97-3-y4-a%c2%97-3-and-p2-a%c2%97-3-the-order-of-pxty-1-ptt-will-be-a-2-a%c2%97-2-b-3-a%c2%97-3-c-4-a%c2%97-3-d-3-a%c2%97-4\/","title":{"rendered":"Consider the matrices X(4 \u00c3\u0097 3), Y(4 \u00c3\u0097 3) and P(2 \u00c3\u0097 3). The order of [P(XTY)-1 PT]T will be A. (2 \u00c3\u0097 2) B. (3 \u00c3\u0097 3) C. (4 \u00c3\u0097 3) D. (3 \u00c3\u0097 4)"},"content":{"rendered":"

[amp_mcq option1=”(2 \u00c3\u0097 2)” option2=”(3 \u00c3\u0097 3)” option3=”(4 \u00c3\u0097 3)” option4=”(3 \u00c3\u0097 4)” correct=”option1″]<\/p>\n

The correct answer is (3 \u00c3\u0097 4).<\/p>\n

The order of a matrix is the number of rows in the matrix by the number of columns in the matrix. For example, a matrix with 3 rows and 4 columns would have an order of $(3\\times4)$.<\/p>\n

In this question, we are given the matrices $X$, $Y$, and $P$, where $X$ is a $(4\\times3)$ matrix, $Y$ is a $(4\\times3)$ matrix, and $P$ is a $(2\\times3)$ matrix.<\/p>\n

We are asked to find the order of the matrix $[P(XTY)^{-1}PT]^T$.<\/p>\n

To find the order of this matrix, we can first find the order of the matrix $P(XTY)^{-1}$.<\/p>\n

The order of $P(XTY)^{-1}$ is the same as the order of $XTY$, which is $(4\\times3)$.<\/p>\n

The order of $[P(XTY)^{-1}PT]^T$ is the transpose of the order of $P(XTY)^{-1}$, which is $(3\\times4)$.<\/p>\n

Therefore, the order of $[P(XTY)^{-1}PT]^T$ is $(3\\times4)$.<\/p>\n

Here is a brief explanation of each option:<\/p>\n