2.1 Addition, Subtraction and Multiplication of Matrices 矩阵的加减法和乘法 - 独中课程 | 线上补习

高二数学 | 高级数学

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2.1 Addition, Subtraction and Multiplication of Matrices 矩阵的加减法和乘法

[1]

Given that A= $\left(\begin{matrix}3&-5\\1&-2\\\end{matrix}\right)$ . Find matrix B if

已知A= $\left(\begin{matrix}3&-5\\1&-2\\\end{matrix}\right)$ . 求矩阵 B若

[a] 4A – B = 2I

[b] B = A $^2$

[c] AB = I

Answer :

(a) $\left(\begin{matrix}10&-20\\4&-10\\\end{matrix}\right)$

(b) $\left(\begin{matrix}4&-5\\1&-1\\\end{matrix}\right)$

[2]

Given that M = $\left(\begin{matrix}2&-3\\0&4\\\end{matrix}\right)$ , and N = $\left(\begin{matrix}5&1\\2&6\\\end{matrix}\right)$ . If MN + 5X = N, where X is a 2 x 2 matrix, find the matrix X.

已知M = $\left(\begin{matrix}2&-3\\0&4\\\end{matrix}\right)$ , 和 N = $\left(\begin{matrix}5&1\\2&6\\\end{matrix}\right)$ . 若MN + 5X = N, 其中X 是一 2 x 2 矩阵, 求矩阵 X.

Answer :

$\left(\begin{matrix}{\frac{1}{5}}&{\frac{17}{5}}\\-{\frac{6}{5}}&-{\frac{18}{5}}\\\end{matrix}\right)$

[3]

Given A = $\left(\begin{matrix}1\\-1\\\end{matrix}\right)$ , B = $\left(\begin{matrix}1&3\\\end{matrix}\right)$ , C = $\left(\begin{matrix}0&2\\-1&3\\\end{matrix}\right)$ and D = $\left(\begin{matrix}3&0&1\\1&-2&-1\\\end{matrix}\right)$ . Find the matrix

已知 A = $\left(\begin{matrix}1\\-1\\\end{matrix}\right)$ , B = $\left(\begin{matrix}1&3\\\end{matrix}\right)$ , C = $\left(\begin{matrix}0&2\\-1&3\\\end{matrix}\right)$ 和 D = $\left(\begin{matrix}3&0&1\\1&-2&-1\\\end{matrix}\right)$ . 求矩阵

[a] AB
[b] BA
[c] BC
[d] CD

Answer :

(a) $\left(\begin{matrix}1&3\\-1&-3\\\end{matrix}\right)$

(b) (– 2)

(d) $\left(\begin{matrix}2&-4&-2\\0&-6&-4\\\end{matrix}\right)$

[4]

$A=\left(\begin{matrix}1&-2\\0&3\\\end{matrix}\right)$ , $B=\left(\begin{matrix}1&-1&0\\2&2&1\\\end{matrix}\right)$ , $C=\left(\begin{matrix}-1&8\\3&1\\0&2\\\end{matrix}\right)$ , find 求

[a] AB

[b] ABC

[c] BCA

[d] (AB)’

Answer :

(a) $\left(\begin{matrix}-3&-5&-2\\6&6&3\\\end{matrix}\right)$

(b) $\left(\begin{matrix}-12&-33\\12&60\\\end{matrix}\right)$

(d) $\left(\begin{matrix}-3&6\\-5&6\\-2&3\\\end{matrix}\right)$

[5]

Given that A = $\left(\begin{matrix}1&0\\2&3\\\end{matrix}\right)$ , B = $\left(\begin{matrix}p&-1\\r&q\\\end{matrix}\right)$ , and C = $\left(\begin{matrix}-3&4\\0&1\\\end{matrix}\right)$ . If A $^2$ + kC = B, find the values of k, p, q and r.

已知 A = $\left(\begin{matrix}1&0\\2&3\\\end{matrix}\right)$ , B = $\left(\begin{matrix}p&-1\\r&q\\\end{matrix}\right)$ , 和 C = $\left(\begin{matrix}-3&4\\0&1\\\end{matrix}\right)$ . 若 A $^2$ + kC = B, 求 k, p, q 和 r 的值。.

Answer :

$-\frac{1}{4}$ ,

$1\frac{3}{4}$ ,

$8\frac{3}{4}$ ,