whatever

whatever

pronoun

take whatever you want

whatever he says, they won’t believe him

adjective

There’s no evidence whatever to support your theory.

adverb

go see a movie, watch TV,—whatever

whatsoever

whatsoever

pronoun or adjective

• whatever

matter-of-fact

matter-of-fact

adjective

All his life Paul Dirac had a simple and matter-of-fact way of talking.

half-truth

half-truth

noun

Unfortunately this is only a half-truth.

longan

longan

noun

gulp

gulp

verb

She told him not to gulp his food.

introverted

introverted

adjective

a quiet, introverted child who likes to sit at home and read books

Even Ehrenfest, with his keen interest in people, had been unable to get the introverted Dirac to open up. - The Quantum Ten: A Story of Passion, Tragedy, Ambition and Science, by Sheilla Jones

tacit

tacit

adjective

tacit consent

Magic requires tacit cooperation of the audience with the magician—an abandonment of skepticism … the willing suspension of disbelief. — Carl Sagan, The Demon-Haunted World, 1996

crunch

crunch

noun

Crunch, crunch, crunch, his feet sank into the snow.

interdisciplinary

interdisciplinary

adjective

Modern mathematics is a very social, networked experience. The trend is very much towards interdisciplinary, highly collaborative research. - Terence Tao

retell

retell

verb

The movie retells the story of Romeo and Juliet.

paddle

paddle

noun

table tennis paddle

pothole

pothole

noun

by and large

by and large

adverb

But by and large, the American people are good people. — ABC News, 28 Dec. 2025

canola

canola

noun

canola oil

Use canola oil or another neutral cooking oil in place of olive oil. — Kimberly Holland, Southern Living, 13 Dec. 2025

quintessential

quintessential

adjective

Beethoven is considered the quintessential bridge between the Classical and Romantic eras.

Heisenberg was the quintessential handsome German lad, fair-haired and blue-eyed. - The Quantum Ten, by Sheilla Jones

slop

slop

noun

The rise of AI has raised concerns about low-quality content, aka “AI slop.”

watching the usual slop on TV

cleaned the slops out of the cow barn

verb

She slopped coffee on her sweater.

technocrat

technocrat

noun

Carney is ideologically characterized as a centrist, technocrat, and a Blue Grit Liberal.

beacon

beacon

noun

These countries are beacons of democracy.

frosty

frosty

adjective

Frosty the Snowman

cordial

cordial

adjective

a cordial welcome

flounder

flounder

noun

saury

saury

noun

puffer fish

puffer fish

noun

tuna

tuna

noun

lemur

lemur

noun

meerkat

meerkat

noun

bald

bald

adjective

He covered his bald head with a baseball cap.

He had gone completely bald by the age of 30.

Bald eagle nests are often very large in order to compensate for size of the birds. The largest recorded nest was found in Florida in 1963, and was measured at 2.9 m (9.5 ft) wide and 6.1 m (20 ft) deep.

by Ella Wheeler Wilcox

Laugh, and the world laughs with you;
Weep, and you weep alone;
For the sad old earth must borrow its mirth,
But has trouble enough of its own.
Sing, and the hills will answer;
Sigh, it is lost on the air;
The echoes bound to a joyful sound,
But shrink from voicing care.

Rejoice, and men will seek you;
Grieve, and they turn and go;
They want full measure of all your pleasure,
But they do not need your woe.
Be glad, and your friends are many;
Be sad, and you lose them all,—
There are none to decline your nectared wine,
But alone you must drink life’s gall.

Feast, and your halls are crowded;
Fast, and the world goes by.
Succeed and give, and it helps you live,
But no man can help you die.
There is room in the halls of pleasure
For a large and lordly train,
But one by one we must all file on
Through the narrow aisles of pain.

---

Solitude

by Lynette Roberts

She left the hut and bright log fire at noon
And walked outside on crisp white winter snow
To find the iced slopes shadowed like the moon,
The wild wood desolate and bare below;
The red trees wet, adrift with icy flow,
The evergreens with glassy needled leaves;
A bloodstone veined red and white this view weaves.

But lifted off the path like crystal spheres
There lay cut prints of glinting stylised forms
Of birds not seen, large sparkling twig-like spears,
And squirrel pricks where fox’s paw transforms
White single roses out of petal storms;
While keltic scrolls transcribe where birds had been:
Then stamped in ice another track was seen.

A slight right turn of foot. She sensed him there,
Tree like with raincoat shouldered, fine large looks,
A four-armed god. From this sweet honeyed snare
She turned, upspraying, Marsh Tits, Finch and Rooks,
Through brushwood hills, seeing by frosted brooks
His footprints: these she retraced like a bride
With loaves and wood returned to his keen side.

---

• Winter Walk
• Poem of the week: Winter Walk by Lynette Roberts

Oxford Dictionaries

The Oxford Word of the Year 2025 is rage bait

Collins

The Collins Word of the Year 2025 is vibe coding

The Cambridge Dictionary

The Cambridge Dictionary Word of the Year 2025 is parasocial

If a job’s worth doing, it’s worth doing well.

No sweet without sweat.

No pains, no gains.

He that is once born, once must die.

No man knows when he shall die, although he knows he must die.

A dead bee makes no honey.

A dead mouse feels no cold.

Dead dogs bark not.

Praise a fair day at night.

Men fear death as children fear to go in the dark.

We must live by the living, not by the dead.

The devil is not black as he is painted.

Sooner begun, sooner done.

No time like the present.

One good turn deserves another.

Good hand, good hire.

Like fault, like punishment.

Such answer as man gives, such will he get.

Every man after his fashion.

Every one to his taste.

So many men, so many options.

All roads lead to Rome.

Diligence makes an expert workman.

Business is the salt of life.

No bees, no honey; no work, no money.

First come, first served.

Early to bed and early to rise, makes a man healthy, wealthy and wise.

Bread is the staff of life.

The belly carries the legs.

Eat to live and not live to eat.

After dinner sit awhile, after supper walk a mile.

An apple a day keeps the doctor away.

There is no royal road to learning.

Never too late to learn.

Everything must have a beginning.

Everything has an end.

Garbage in, garbage out.

Practise what you preach.

Example is better than precept.

Practice makes perfect.

Keep your mouth shut and your eyes open.

Let bygones be bygones.

A friend in need is a friend indeed.

God helps them that help themselves.

A good heart conquers ill fortune.

All happiness is in the mind.

Laughter is the best medicine.

A merry heart goes all the way.

Great hopes make great men.

Hope for the best.

Tomorrow is another day.

Every man has his faults.

To err is human.

Forgive and forget.

Every path has a puddle.

Life is short and time is swift.

Life begins at forty.

It is easy to be wise after the event.

Better be safe than sorry.

Everyman for himself, and God for us all.

Skill is no burden.

A little body often harbours a great soul.

Many small maka a great.

Time and tide wait for no man.

Now is now, and then was then.

Travel broadens the mind.

The language of truth is simple.

It is too late to call back yesterday.

Time flies.

Time will tell.

Times change and we with them.

be supposed to

You are supposed to listen to your parents.

slip/escape someone’s mind

His name slips/escapes my mind at the moment.

pay off

I finally paid off the loan.

beat the rush

I suggested that we get there by 11:30 to beat the lunchtime rush.

miss the boat

missed the boat on buying stock in the company early on

kettle of fish

I’m used to paddling, but those rapids are a whole other kettle of fish.

snowsuit

snowsuit

noun

arrogance

arrogance

noun

Programming is the best antidote to arrogance I’ve come across — I make so many errors that I am continually reminded of my own fallibility.

gut

gut

noun

The guts uphold the heart, and not the heart the guts.

ballpoint pen

ballpoint pen

noun

curiosity

curiosity

noun

Curiosity killed the cat.

Curiosity is endless, restless, and useless.

chip

chip

noun

The best carpenter makes the fewest chips.

wood chips were spread over the ground between the plants

caravan

caravan

noun

bought a caravan and drove cross-country to California

toadstool

toadstool

noun

• a fungus that has an umbrella-shaped cap, one that is poisonous or unfit for food

A toadstool generally refers to a poisonous mushroom.

schoolchild

schoolchild

noun

Almost every schoolchild in America learns Lincoln was born in a Kentucky log cabin. — Frank Witsil, Detroit Free Press, 13 July 2023

soggy

soggy

adjective

Be sure to keep the soil moist but not soggy. — Sheryl Geerts, Better Homes & Gardens, 15 Dec. 2025

pal

pal

noun

We’ve been pals since we were kids.

after all, tomorrow is another day

don’t worry, be happy

every home should have one!

give me a hug

if anything can go wrong, it will

It’s good to talk

master of your domain

never mind

where’s the beef?

1 Matrices

Section 1 The Basic Operations

1.1. What are the entries \( a_{21} \), and \( a_{23} \) of the matrix A = \( \begin{bmatrix}
1 &2 &5 \\
2 &7 &8 \\
0 &9 &4
\end{bmatrix} \) ?

\( a_{21} = 2 \), and \( a_{23} = 8 \)

1.2. Determine the products AB and BA for the following values of A and B:

\( A = \begin{bmatrix}
1 &2 &3 \\
3 &3 &1
\end{bmatrix}, \hspace{2mm}
B = \begin{bmatrix}
-8 &-4 \\
9 &5 \\
-3 &-2
\end{bmatrix} \)

\( AB = \begin{bmatrix}
1 &0 \\
0 &1
\end{bmatrix}, \hspace{4mm}
BA = \begin{bmatrix}
-20 &-28 &-28 \\
24 &33 &32 \\
-9 &-12 &-11
\end{bmatrix} \)

\(
A = \begin{bmatrix}
1 &4 \\
1 &2
\end{bmatrix}, \hspace{2mm}
B = \begin{bmatrix}
6 &-4 \\
3 &2
\end{bmatrix}
\)

\( AB = \begin{bmatrix}
18 &4 \\
12 &0
\end{bmatrix}, \hspace{4mm}
BA = \begin{bmatrix}
2 &16 \\
5 &16
\end{bmatrix} \)

1.4. Verify the associative law for the matrix product

\( ABC = \begin{bmatrix}
1 &2 \\
0 &1
\end{bmatrix}
\begin{bmatrix}
0 &1 &2 \\
1 &1 &3
\end{bmatrix}
\begin{bmatrix}
1 \\
4 \\
3
\end{bmatrix} \)

Note: This is a self-checkingproblem.It won’t come out unless you multiply correctly. If you need to practice matrix multiplication, use this problem as a model.

\( (AB)C = \begin{bmatrix}
2 &3 &8 \\
1 &1 &3
\end{bmatrix}
\begin{bmatrix}
1 \\
4 \\
3
\end{bmatrix}
= \begin{bmatrix}
38 \\
14
\end{bmatrix}
= 2 \begin{bmatrix}
19 \\
7
\end{bmatrix}
\)

\( A(BC) = \begin{bmatrix}
1 &2 \\
0 &1
\end{bmatrix}
\begin{bmatrix}
10 \\
14
\end{bmatrix}
= \begin{bmatrix}
38 \\
14
\end{bmatrix}
= 2 \begin{bmatrix}
19 \\
7
\end{bmatrix}
\)

Far from eye, far from heart.

Friends agree best at a distance.

Out of sight, out of mind.

Long absent, soon forgotten.

Nothing seek, nothing find.

Anger punishes itself.

A hungry man is an angry man.

Fear of death is worse than death itself.

He laughs best who laughs last.

The unexpected always happens.

Never judge from apperances.

Better to ask the way than go astray.

Like question, like answer.

It is not every question that deserves an answer.

Every beginning is hard.

Such beginning, such end.

Nurture is above nature.

Nurture and good manners maketh man.

Manners and money make a gentleman.

‘After you’ is good manners.

Curiosity is ill manners in another house.

Better the devil you know than the devil you don’t know.

There is nothing permannent except change.

There is nothing new under the sun.

The apple never falls far from the tree.

Boys will be men.

You pays your money and you takes your choice.

The customer is always right.

Content is happiness.

A little bird is content with a little nest.