Practice the questions given in the Worksheet on Matrix Multiplication.
1. Let A = \(\begin{bmatrix} -10 & 1\\ 3 & -2 \end{bmatrix}\), B = \(\begin{bmatrix} 6\\ -7 \end{bmatrix}\). Find AB and BA if possible.
2. Let A = \(\begin{bmatrix} 1 & -1\\ 3 & 4 \end{bmatrix}\), B = \(\begin{bmatrix} 0 & 1\\ 2 & -3 \end{bmatrix}\).
(i) Find AB and BA if possible.
(ii) Verify if AB = BA.
(iii) Find A2.
(iv) Find AB2.
3. If A = \(\begin{bmatrix} sin \, \, 30^{\circ} + cos \, \, 60^{\circ} & tan \, \, 45^{\circ} - cot \, \, 45^{\circ}\\ cos \, \, 90^{\circ} & sin \, \, 90^{\circ} \end{bmatrix}\) then prove that A3 = A2 =A.
4. If A = \(\begin{bmatrix} cos \, \, \theta & -sin \, \, \theta\\ sin \, \, \theta & cos \, \, \theta \end{bmatrix}\) and B = \(\begin{bmatrix} cos \, \, \theta & sin \, \, \theta\\ -sin \, \, \theta & cos \, \, \theta \end{bmatrix}\), then prove that AB = I, where I is the unit matrix.
5. Let A = \(\begin{bmatrix} -2 & 9\\ 1 & 3 \end{bmatrix}\), B = \(\begin{bmatrix} 1 & 1\\ 1 & 1 \end{bmatrix}\) and C = \(\begin{bmatrix} -1 & 2\\ 3 & -1 \end{bmatrix}\).
(i) Find (AB)C.
(ii) Prove that A(BC) = (AB)C.
Answer:
1. AB = \(\begin{bmatrix} -67\\ 32 \end{bmatrix}\); BA is not possible because number of columns in B ≠ number of rows in A
2. (i) AB = \(\begin{bmatrix} -2 & 4\\ 8 & -9 \end{bmatrix}\); B = \(\begin{bmatrix} 3 & 4\\ -7 & -14 \end{bmatrix}\)
(ii) AB ≠ BA.
(iii) \(\begin{bmatrix} -2 & -5\\ 15 & 13 \end{bmatrix}\)
(iv) \(\begin{bmatrix} 8 & -14\\ -18 & 35 \end{bmatrix}\)
5. (i) \(\begin{bmatrix} 14 & 7\\ 8 & 4 \end{bmatrix}\)
From Worksheet on Matrix Multiplication to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Dec 03, 24 01:29 AM
Dec 03, 24 01:19 AM
Dec 02, 24 01:47 PM
Dec 02, 24 01:26 PM
Nov 29, 24 01:26 AM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.