题目
题目

ETF2700 - ETF5970 - S2 2025 Quiz 2

数值题

Define the matrices A=\left[\begin{array}{ccc} 2&3\\ {1}&{-5}\end{array}\right] and B=\left[\begin{array}{ccc} 4&3&6\\ {1}&2.8&3\end{array}\right]. What is the entry in the first row and second column of AB?

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思路分析
To find the (1,2) entry of AB, I’ll multiply the first row of A by the second column of B. First, ident......Login to view full explanation

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Vector a =  10      12 And vector b =  2 3   Whats the value of a*b ?  (* is matrix multiplication);  Please enter a number with no decimals.  

Question at position 13 [1−12][[4−10][23]+[1001−11]]=\begin{bmatrix} 1 & -1 & 2 \\ \end{bmatrix} \left[ \begin{bmatrix} 4 \\ -1\\ 0 \end{bmatrix} \begin{bmatrix} 2 &3 \\ \end{bmatrix} + \begin{bmatrix} 1 & 0 \\ 0 & 1 \\ -1 & 1 \end{bmatrix} \right] =[2−34810]\begin{bmatrix} 2 & -3 \\ 4 & 8 \\ 1 & 0 \end{bmatrix}none of the above[29−3]\begin{bmatrix} 2 & 9 & -3 \\ \end{bmatrix}[5−7]\begin{bmatrix} 5 \\ -7 \end{bmatrix}[912]\begin{bmatrix} 9 & 12 \\ \end{bmatrix}

Question at position 12 [1−134][025−3]=\begin{bmatrix} 1 & -1 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} 0 & 2 \\ 5 & -3 \end{bmatrix} =[−5520−6]\begin{bmatrix} -5 & 5 \\ 20 & -6 \end{bmatrix}[68−4−17]\begin{bmatrix} 6 & 8 \\ -4 & -17 \end{bmatrix}[−2838]\begin{bmatrix} -2 & 8 \\ 3 & 8 \end{bmatrix}[4−106]\begin{bmatrix} 4 & -1 \\ 0 & 6 \end{bmatrix}[0−215−12]\begin{bmatrix} 0 & -2 \\ 15 & -12 \end{bmatrix}

Consider the matrix: \[ \mathbf {X=}\begin {pmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 0 \\ 1 & 0 & 1 \end {pmatrix}.\]Which one of the following matrices is \(\mathbf {X}’\mathbf {X}\)?

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